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The student will learn to find the slope of a line given two points on a graph or explicitly given the points. Slope is defined as the steepness or rise over run of a line between two points. You can find the slope by taking the difference in the y-values and dividing by the difference in the x-values of the two points. Slope can be positive, negative, zero if horizontal, or undefined if vertical. Examples are worked through of finding the slope given two points on a graph or the points explicitly.

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Writing Equations of a Line

1) The document discusses various forms of equations for lines, including slope-intercept form, standard form, and point-slope form. It provides definitions and examples of writing equations of lines given the slope and y-intercept or given two points on the line.
2) Key concepts covered include writing the equation of a line given its slope m and y-intercept b using slope-intercept form y=mx+b, or given slope m and a point (x1,y1) using point-slope form y-y1=m(x-x1).
3) Examples are provided for writing equations of lines using slope-intercept form when given slope and y-intercept, and using point-

Synthetic division

This document provides instructions for using synthetic division to divide polynomials. It contains the following key points:
1. Synthetic division can be used to divide polynomials when the divisor has a leading coefficient of 1 and there is a coefficient for every power of the variable in the numerator.
2. The procedure involves writing the terms of the numerator in descending order, bringing down the constant of the divisor, multiplying and adding down the columns to obtain the coefficients of the quotient polynomial and the remainder.
3. An example problem walks through each step of synthetic division to divide (5x^4 - 4x^2 + x + 6) / (x - 3), obtaining a quotient of 5x^3 + 15

Graph of linear equations

This document discusses four methods for graphing linear equations on a coordinate plane:
1. Using any two points on the line.
2. Using the x-intercept and y-intercept.
3. Using the slope and y-intercept.
4. Using the slope and one known point.
Examples are provided to illustrate each method. Graphing linear equations is important for visualizing relationships between variables in real-life situations.

Slope of a Line

This document contains a lesson on slope of a line from a mathematics course. It includes examples of calculating slope given two points on a line, identifying whether graphs represent constant or variable rates of change, and word problems applying slope to real-world contexts like cost of fruit and gas. The key points are that slope is defined as the ratio of rise over run, or change in y over change in x, and represents the constant rate of change for linear equations and functions.

Graphing linear equations

There are three main forms for writing linear equations: slope-intercept form (y=mx+b), point-slope form (y-y1=m(x-x1)), and standard form (Ax + By = C). Each form can be used to graph the line by finding ordered pairs that satisfy the equation and plotting those points. For slope-intercept form, a table of x-values with their corresponding y-values is made to find the points. For point-slope form and standard form, the given point and slope or intercepts are used to find another point which are then plotted and connected with a line.

Finding the slope of a line

This document defines slope and discusses how to calculate it using the rise over run method. Slope is the ratio of vertical change to horizontal change between two points on a line. It provides examples of finding the slopes of various lines by calculating rise over run. The document concludes by explaining that if you know the slope and one point, you can draw the line. It provides examples of drawing lines given the slope and a point.

Division Of Polynomials

Division of polynomials follows the same rules as division of real numbers. To divide a polynomial by a monomial, each term of the dividend is divided by the monomial divisor. To divide a polynomial by a polynomial, long division is used by repeatedly determining the quotient and remainder until the division is complete. The steps of long division are shown through an example of dividing a third degree polynomial by a linear polynomial divisor. The quotient and remainder are checked by multiplying the divisor and quotient together.

point slope form

This document discusses using the point-slope form to find the equation of a line given a slope and point. It provides the point-slope form equation, and examples of finding the line equation for different slopes and points. Exercises are provided for the reader to practice finding additional line equations using given slopes and points.

Writing Equations of a Line

1) The document discusses various forms of equations for lines, including slope-intercept form, standard form, and point-slope form. It provides definitions and examples of writing equations of lines given the slope and y-intercept or given two points on the line.
2) Key concepts covered include writing the equation of a line given its slope m and y-intercept b using slope-intercept form y=mx+b, or given slope m and a point (x1,y1) using point-slope form y-y1=m(x-x1).
3) Examples are provided for writing equations of lines using slope-intercept form when given slope and y-intercept, and using point-

Synthetic division

This document provides instructions for using synthetic division to divide polynomials. It contains the following key points:
1. Synthetic division can be used to divide polynomials when the divisor has a leading coefficient of 1 and there is a coefficient for every power of the variable in the numerator.
2. The procedure involves writing the terms of the numerator in descending order, bringing down the constant of the divisor, multiplying and adding down the columns to obtain the coefficients of the quotient polynomial and the remainder.
3. An example problem walks through each step of synthetic division to divide (5x^4 - 4x^2 + x + 6) / (x - 3), obtaining a quotient of 5x^3 + 15

Graph of linear equations

This document discusses four methods for graphing linear equations on a coordinate plane:
1. Using any two points on the line.
2. Using the x-intercept and y-intercept.
3. Using the slope and y-intercept.
4. Using the slope and one known point.
Examples are provided to illustrate each method. Graphing linear equations is important for visualizing relationships between variables in real-life situations.

Slope of a Line

This document contains a lesson on slope of a line from a mathematics course. It includes examples of calculating slope given two points on a line, identifying whether graphs represent constant or variable rates of change, and word problems applying slope to real-world contexts like cost of fruit and gas. The key points are that slope is defined as the ratio of rise over run, or change in y over change in x, and represents the constant rate of change for linear equations and functions.

Graphing linear equations

There are three main forms for writing linear equations: slope-intercept form (y=mx+b), point-slope form (y-y1=m(x-x1)), and standard form (Ax + By = C). Each form can be used to graph the line by finding ordered pairs that satisfy the equation and plotting those points. For slope-intercept form, a table of x-values with their corresponding y-values is made to find the points. For point-slope form and standard form, the given point and slope or intercepts are used to find another point which are then plotted and connected with a line.

Finding the slope of a line

This document defines slope and discusses how to calculate it using the rise over run method. Slope is the ratio of vertical change to horizontal change between two points on a line. It provides examples of finding the slopes of various lines by calculating rise over run. The document concludes by explaining that if you know the slope and one point, you can draw the line. It provides examples of drawing lines given the slope and a point.

Division Of Polynomials

Division of polynomials follows the same rules as division of real numbers. To divide a polynomial by a monomial, each term of the dividend is divided by the monomial divisor. To divide a polynomial by a polynomial, long division is used by repeatedly determining the quotient and remainder until the division is complete. The steps of long division are shown through an example of dividing a third degree polynomial by a linear polynomial divisor. The quotient and remainder are checked by multiplying the divisor and quotient together.

point slope form

This document discusses using the point-slope form to find the equation of a line given a slope and point. It provides the point-slope form equation, and examples of finding the line equation for different slopes and points. Exercises are provided for the reader to practice finding additional line equations using given slopes and points.

Equations of a line ppt

To write the equation of a line in slope-intercept form (y=mx+b) given the slope (m) and y-intercept (b):
1) Identify the y-intercept as the y-value when x=0
2) Plug the slope (m) and y-intercept (b) into the slope-intercept equation
3) To write the equation when given two points, use the point-slope formula: y-y1=m(x-x1), where m is the slope calculated from the two points.

Linear Equations in Two Variables

The document discusses linear equations in two variables. It defines a linear equation as one that can be written in the standard form Ax + By = C, where A, B, and C are real numbers and A and B cannot both be zero. Examples are provided of determining if equations are linear and identifying the A, B, and C components if they are linear. The document also discusses using ordered pairs as solutions to linear equations and finding multiple solutions to a given linear equation.

Identifying slope and y intercept

The document discusses the equation of a line, y=mx+b, and its key components of slope and y-intercept. It defines slope as the rate of rise or fall of a line and provides the formula to calculate it between two points. It also defines the y-intercept as the point where the line crosses the y-axis. The document provides examples of lines with their slopes and y-intercepts calculated from points and used to write the equation of the line.

Direct Variation

Direct variation describes the relationship between two quantities where one quantity varies as the other changes proportionally. It can be represented by the equation y = kx, where k is the constant of variation.
Some key points about direct variation:
- The graph of a direct variation will pass through the origin, as there is no y-intercept term.
- To determine if a relationship represents direct variation, calculate the constant of variation k from the data and check if it remains the same for different values.
- Direct variation can be used to find unknown values by setting up a table with the known values and using the direct variation equation y = kx.

Solving of system of linear inequalities

This document discusses linear inequalities in two variables and their graphical representations. It can be summarized as:
1) A linear inequality in two variables has infinitely many solutions that can be represented on a coordinate plane as all points on one side of a boundary line.
2) The graph of a linear inequality consists of all points in a region called a half-plane, bounded by the boundary line. Points on one side of the line are solutions while points on the other side are not solutions.
3) To solve a system of linear inequalities, the inequalities are graphed on the same grid. The solution set contains all points in the region where the graphs overlap, and any points on solid boundary

2/27/12 Special Factoring - Sum & Difference of Two Cubes

The document is about factoring polynomials, specifically factoring the sum and difference of cubes. It provides the formulas for factoring the sum and difference of cubes, along with examples of factoring expressions using those formulas. It also discusses factoring out the greatest common factor from polynomials.

Linear equation in 2 variables

This document provides information about linear equations in two variables. It defines a linear equation as one that can be written in the form ax + by + c = 0, where a, b, and c are real numbers and a and b are not equal to 0. It discusses using the rectangular coordinate system to graph linear equations by plotting the x- and y-intercepts. It also describes how to determine if an ordered pair is a solution to a linear equation by substituting the x- and y-values into the equation. Finally, it briefly outlines common methods for solving systems of linear equations, including elimination, substitution, and cross-multiplication.

System of linear inequalities

Here is the system of inequalities for the cross-country team problem:
Let x = number of water bottles sold to students
Let y = number of water bottles sold to others
x + y ≤ 100 (they have 100 bottles total)
3x + 5y ≥ 400 (they need at least $400)
Graph the regions defined by these inequalities and the overlapping region is the solution.

Graphing Linear Functions

This document provides instructions on graphing lines by plotting ordered pairs on a coordinate plane. It explains that an ordered pair consists of two numbers in parentheses separated by a comma, with the first number representing the x-coordinate and the second representing the y-coordinate. It then discusses how to plot points by starting at the origin (0,0) and moving left/right along the x-axis and up/down along the y-axis. The document also covers how to graph lines by plotting points from a table of x-y values and connecting them. It introduces the concept of slope as the steepness of a line and how to calculate it between two points using the rise over run formula.

Adding and subtracting rational expressions

Using rules for fractions, rational expressions can be added and subtracted by finding common denominators. To find the common denominator, we find the least common multiple (LCM) of the denominators. With polynomials, the LCM will contain all factors of each denominator. We can then convert the fractions to equivalent forms using the LCM as the new denominator before combining like terms to evaluate the expression. Special cases may involve fractions with understood denominators of 1 or similar but non-equal denominators that can be made equal through factoring.

Multiplying polynomials

The document describes three methods for multiplying polynomials:
1) The distributive property, which involves multiplying each term of one polynomial with each term of the other.
2) FOIL (First, Outer, Inner, Last), which is a mnemonic for multiplying binomials by multiplying corresponding terms.
3) The box method, which involves drawing a box and writing one polynomial above and beside the box, then multiplying corresponding terms. Examples are provided to demonstrate each method.

Equation Of A Line

This document discusses different methods for finding the equation of a line, including:
1) Given the slope and y-intercept
2) Using a graph
3) Given a point and the slope
4) Given two points
It provides examples of how to write the line equation using each method.

6.7 quadratic inequalities

This document discusses how to graph and solve quadratic inequalities. It provides steps for graphing quadratic inequalities by sketching the parabola and shading the appropriate region based on a test point. Examples are given of solving quadratic inequalities graphically by determining the portions of the graph above or below the x-axis and obtaining the solution intervals. Exercises are also worked through to practice solving quadratic inequalities graphically.

Math 8 - Linear Functions

This document discusses linear functions and how to represent them using equations, graphs, and tables of values. It defines a linear function as one that can be written in the form f(x) = mx + b, where m is the slope and b is the y-intercept. Examples are provided to illustrate determining the slope and y-intercept from an equation and representing a linear function using an equation, table of values, or graph. It is explained that a linear function will produce a straight line on a graph and have constant differences in x- and y-coordinates in its table of values.

System of Linear inequalities in two variables

This document provides instructions for solving systems of linear inequalities in two variables by graphing. It defines a system of inequalities and explains that the solution is the region where the graphs of the inequalities overlap. A step-by-step process is outlined: 1) graph each inequality individually, 2) shade the appropriate half-plane, 3) the overlapping shaded regions represent the solution. An example system is graphed to demonstrate. Students will evaluate by being assigned a system to graph and answer related questions about the solution region.

Linear functions

This document defines and provides examples of linear functions. It begins by stating the objective is to define and describe linear functions using points and equations. It then defines that a linear function is of the form f(x)=mx+b, where m is the slope and b is the y-intercept. Several examples are provided to illustrate identifying if a function is linear and calculating its slope and y-intercept. The document also discusses rewriting linear equations between the standard and slope-intercept forms.

Translating Expressions

The document provides examples and explanations for translating word problems and phrases into algebraic expressions. It gives examples such as "18 less than a number" being translated to "x - 18" and "the product of a number and 5" being "5n". It also provides word problems like writing an expression for the total cost of admission plus rides at a county fair. The document teaches learners how to identify keywords that indicate mathematical operations when translating word phrases into algebraic notation.

Chapter 5 Point Slope Form

The document provides examples and explanations for writing linear equations in point-slope and slope-intercept form given the slope and a point, or two points on the line. It includes warm-up questions, examples with step-by-step solutions for writing equations from graphical and numerical information, and a problem applying the concepts to a real-world situation. Practice problems assess understanding of writing linear equations from geometric or tabular data.

Lecture 05 b radicals multiplication and division

This document discusses multiplying and dividing radical expressions. It provides examples of multiplying radicals with the same index by multiplying coefficients and radicands separately. It explains how to divide radicals by dividing coefficients and radicands, and rationalizing denominators by multiplying the numerator and denominator by a number to eliminate radicals in the denominator. The document also demonstrates multiplying radicals with different indices by applying the distributive property and keeping track of indices.

Variable and Algebraic Expressions

1. The document provides examples and explanations for evaluating algebraic expressions by substituting values for variables.
2. It gives examples of evaluating expressions involving addition, subtraction, multiplication, division, and order of operations.
3. Students are asked to evaluate expressions for given variable values to check their understanding.

Slope

The document provides information about calculating the slope of a line from a graph or two points, including examples and practice problems. Key terms are defined, such as rise, run, slope, dependent and independent variables. An example problem demonstrates how to find the slope from a table of gas costs and gallons and interpret what the slope represents. A lesson quiz provides practice finding slopes and interpreting what they represent based on graphs and tables.

Slopes in the real world url

The document defines different types of slopes including positive and negative slopes which refer to an upward or downward slant to the right or left, respectively. It also discusses steeper and flatter slopes compared to positive and negative slopes, as well as zero or horizontal slopes that go straight left to right and undefined or vertical slopes that go straight up and down. The purpose is to provide information on different slope definitions and orientations.

Equations of a line ppt

To write the equation of a line in slope-intercept form (y=mx+b) given the slope (m) and y-intercept (b):
1) Identify the y-intercept as the y-value when x=0
2) Plug the slope (m) and y-intercept (b) into the slope-intercept equation
3) To write the equation when given two points, use the point-slope formula: y-y1=m(x-x1), where m is the slope calculated from the two points.

Linear Equations in Two Variables

The document discusses linear equations in two variables. It defines a linear equation as one that can be written in the standard form Ax + By = C, where A, B, and C are real numbers and A and B cannot both be zero. Examples are provided of determining if equations are linear and identifying the A, B, and C components if they are linear. The document also discusses using ordered pairs as solutions to linear equations and finding multiple solutions to a given linear equation.

Identifying slope and y intercept

The document discusses the equation of a line, y=mx+b, and its key components of slope and y-intercept. It defines slope as the rate of rise or fall of a line and provides the formula to calculate it between two points. It also defines the y-intercept as the point where the line crosses the y-axis. The document provides examples of lines with their slopes and y-intercepts calculated from points and used to write the equation of the line.

Direct Variation

Direct variation describes the relationship between two quantities where one quantity varies as the other changes proportionally. It can be represented by the equation y = kx, where k is the constant of variation.
Some key points about direct variation:
- The graph of a direct variation will pass through the origin, as there is no y-intercept term.
- To determine if a relationship represents direct variation, calculate the constant of variation k from the data and check if it remains the same for different values.
- Direct variation can be used to find unknown values by setting up a table with the known values and using the direct variation equation y = kx.

Solving of system of linear inequalities

This document discusses linear inequalities in two variables and their graphical representations. It can be summarized as:
1) A linear inequality in two variables has infinitely many solutions that can be represented on a coordinate plane as all points on one side of a boundary line.
2) The graph of a linear inequality consists of all points in a region called a half-plane, bounded by the boundary line. Points on one side of the line are solutions while points on the other side are not solutions.
3) To solve a system of linear inequalities, the inequalities are graphed on the same grid. The solution set contains all points in the region where the graphs overlap, and any points on solid boundary

2/27/12 Special Factoring - Sum & Difference of Two Cubes

The document is about factoring polynomials, specifically factoring the sum and difference of cubes. It provides the formulas for factoring the sum and difference of cubes, along with examples of factoring expressions using those formulas. It also discusses factoring out the greatest common factor from polynomials.

Linear equation in 2 variables

This document provides information about linear equations in two variables. It defines a linear equation as one that can be written in the form ax + by + c = 0, where a, b, and c are real numbers and a and b are not equal to 0. It discusses using the rectangular coordinate system to graph linear equations by plotting the x- and y-intercepts. It also describes how to determine if an ordered pair is a solution to a linear equation by substituting the x- and y-values into the equation. Finally, it briefly outlines common methods for solving systems of linear equations, including elimination, substitution, and cross-multiplication.

System of linear inequalities

Here is the system of inequalities for the cross-country team problem:
Let x = number of water bottles sold to students
Let y = number of water bottles sold to others
x + y ≤ 100 (they have 100 bottles total)
3x + 5y ≥ 400 (they need at least $400)
Graph the regions defined by these inequalities and the overlapping region is the solution.

Graphing Linear Functions

This document provides instructions on graphing lines by plotting ordered pairs on a coordinate plane. It explains that an ordered pair consists of two numbers in parentheses separated by a comma, with the first number representing the x-coordinate and the second representing the y-coordinate. It then discusses how to plot points by starting at the origin (0,0) and moving left/right along the x-axis and up/down along the y-axis. The document also covers how to graph lines by plotting points from a table of x-y values and connecting them. It introduces the concept of slope as the steepness of a line and how to calculate it between two points using the rise over run formula.

Adding and subtracting rational expressions

Using rules for fractions, rational expressions can be added and subtracted by finding common denominators. To find the common denominator, we find the least common multiple (LCM) of the denominators. With polynomials, the LCM will contain all factors of each denominator. We can then convert the fractions to equivalent forms using the LCM as the new denominator before combining like terms to evaluate the expression. Special cases may involve fractions with understood denominators of 1 or similar but non-equal denominators that can be made equal through factoring.

Multiplying polynomials

The document describes three methods for multiplying polynomials:
1) The distributive property, which involves multiplying each term of one polynomial with each term of the other.
2) FOIL (First, Outer, Inner, Last), which is a mnemonic for multiplying binomials by multiplying corresponding terms.
3) The box method, which involves drawing a box and writing one polynomial above and beside the box, then multiplying corresponding terms. Examples are provided to demonstrate each method.

Equation Of A Line

This document discusses different methods for finding the equation of a line, including:
1) Given the slope and y-intercept
2) Using a graph
3) Given a point and the slope
4) Given two points
It provides examples of how to write the line equation using each method.

6.7 quadratic inequalities

This document discusses how to graph and solve quadratic inequalities. It provides steps for graphing quadratic inequalities by sketching the parabola and shading the appropriate region based on a test point. Examples are given of solving quadratic inequalities graphically by determining the portions of the graph above or below the x-axis and obtaining the solution intervals. Exercises are also worked through to practice solving quadratic inequalities graphically.

Math 8 - Linear Functions

This document discusses linear functions and how to represent them using equations, graphs, and tables of values. It defines a linear function as one that can be written in the form f(x) = mx + b, where m is the slope and b is the y-intercept. Examples are provided to illustrate determining the slope and y-intercept from an equation and representing a linear function using an equation, table of values, or graph. It is explained that a linear function will produce a straight line on a graph and have constant differences in x- and y-coordinates in its table of values.

System of Linear inequalities in two variables

This document provides instructions for solving systems of linear inequalities in two variables by graphing. It defines a system of inequalities and explains that the solution is the region where the graphs of the inequalities overlap. A step-by-step process is outlined: 1) graph each inequality individually, 2) shade the appropriate half-plane, 3) the overlapping shaded regions represent the solution. An example system is graphed to demonstrate. Students will evaluate by being assigned a system to graph and answer related questions about the solution region.

Linear functions

This document defines and provides examples of linear functions. It begins by stating the objective is to define and describe linear functions using points and equations. It then defines that a linear function is of the form f(x)=mx+b, where m is the slope and b is the y-intercept. Several examples are provided to illustrate identifying if a function is linear and calculating its slope and y-intercept. The document also discusses rewriting linear equations between the standard and slope-intercept forms.

Translating Expressions

The document provides examples and explanations for translating word problems and phrases into algebraic expressions. It gives examples such as "18 less than a number" being translated to "x - 18" and "the product of a number and 5" being "5n". It also provides word problems like writing an expression for the total cost of admission plus rides at a county fair. The document teaches learners how to identify keywords that indicate mathematical operations when translating word phrases into algebraic notation.

Chapter 5 Point Slope Form

The document provides examples and explanations for writing linear equations in point-slope and slope-intercept form given the slope and a point, or two points on the line. It includes warm-up questions, examples with step-by-step solutions for writing equations from graphical and numerical information, and a problem applying the concepts to a real-world situation. Practice problems assess understanding of writing linear equations from geometric or tabular data.

Lecture 05 b radicals multiplication and division

This document discusses multiplying and dividing radical expressions. It provides examples of multiplying radicals with the same index by multiplying coefficients and radicands separately. It explains how to divide radicals by dividing coefficients and radicands, and rationalizing denominators by multiplying the numerator and denominator by a number to eliminate radicals in the denominator. The document also demonstrates multiplying radicals with different indices by applying the distributive property and keeping track of indices.

Variable and Algebraic Expressions

1. The document provides examples and explanations for evaluating algebraic expressions by substituting values for variables.
2. It gives examples of evaluating expressions involving addition, subtraction, multiplication, division, and order of operations.
3. Students are asked to evaluate expressions for given variable values to check their understanding.

Equations of a line ppt

Equations of a line ppt

Linear Equations in Two Variables

Linear Equations in Two Variables

Identifying slope and y intercept

Identifying slope and y intercept

Direct Variation

Direct Variation

Solving of system of linear inequalities

Solving of system of linear inequalities

2/27/12 Special Factoring - Sum & Difference of Two Cubes

2/27/12 Special Factoring - Sum & Difference of Two Cubes

Linear equation in 2 variables

Linear equation in 2 variables

System of linear inequalities

System of linear inequalities

Graphing Linear Functions

Graphing Linear Functions

Adding and subtracting rational expressions

Adding and subtracting rational expressions

Multiplying polynomials

Multiplying polynomials

Equation Of A Line

Equation Of A Line

6.7 quadratic inequalities

6.7 quadratic inequalities

Math 8 - Linear Functions

Math 8 - Linear Functions

System of Linear inequalities in two variables

System of Linear inequalities in two variables

Linear functions

Linear functions

Translating Expressions

Translating Expressions

Chapter 5 Point Slope Form

Chapter 5 Point Slope Form

Lecture 05 b radicals multiplication and division

Lecture 05 b radicals multiplication and division

Variable and Algebraic Expressions

Variable and Algebraic Expressions

Slope

The document provides information about calculating the slope of a line from a graph or two points, including examples and practice problems. Key terms are defined, such as rise, run, slope, dependent and independent variables. An example problem demonstrates how to find the slope from a table of gas costs and gallons and interpret what the slope represents. A lesson quiz provides practice finding slopes and interpreting what they represent based on graphs and tables.

Slopes in the real world url

The document defines different types of slopes including positive and negative slopes which refer to an upward or downward slant to the right or left, respectively. It also discusses steeper and flatter slopes compared to positive and negative slopes, as well as zero or horizontal slopes that go straight left to right and undefined or vertical slopes that go straight up and down. The purpose is to provide information on different slope definitions and orientations.

2.2 linear equations and 2.3 Slope

The document discusses linear equations and slope. It covers plotting points on a coordinate plane, calculating slope using the rise over run formula, writing equations in slope-intercept form, finding the x- and y-intercepts, and graphing lines by making a table or using the slope and y-intercept. Methods are provided for determining the equation of a line given two points, the slope and one point, or from a graph.

Slope in real life!

Slope describes the steepness of a line on the coordinate plane, whether it rises from bottom left to top right (positive slope), top left to bottom right (negative slope), or horizontally across (zero slope). Examples are given of objects that demonstrate each type of slope, such as roads that have positive slope as they go up hills, slides that have negative slope to go down, and shelves that have zero slope horizontally. Steeper slopes are closer to the y-axis, while flatter slopes are closer to the x-axis. Real-world examples like steep hills and flatter golf greens illustrate different degrees of positive and negative slope.

Real life application of slope_Ajay_TD

This document discusses slope and how it is defined as the ratio of the "rise" over the "run" between two points on a line. It provides examples of slope from staircases, buildings, flag poles, pianos, cars, and more to illustrate how slope is represented in the real world. Key terms discussed include positive and negative slope, and that horizontal and vertical lines have slopes of 0 and no slope, respectively.

Two point form Equation of a line

The document provides information about finding the coordinates of points, plotting pairs of points, calculating the slope of lines between points, and obtaining the equation of a line using the two-point form. It gives examples of finding the slope and equation of lines passing through various pairs of points. It also includes examples for students to practice finding the equations of lines from given points.

Slopes in the real world

The document defines different types of slopes including positive slopes which increase from bottom left to top right, negative slopes which decrease from top to bottom, and undefined slopes which are vertical lines. It also describes steeper slopes as steeper than regular positive or negative slopes, zero slopes which have no slope, and flatter slopes which are less steep than usual.

Slope in the real world

The document defines slope as the steepness or incline of a line, and provides examples of different types of slopes, including:
- Positive (increasing) slope, shown through examples like mountains, books propped open, and structures that increase in height.
- Negative slope, shown through descending ramps, broken furniture, and see-saws.
- Steeper slopes, exemplified by steep mountains, ramps, roads, bridges and a church roof.
- Zero slope, where there is no incline or decline, such as flat surfaces.
- Flatter slope, with a minor tilt.
- Undefined slope, where vertical lines have no definition of slope.

Slopes in real life

The document provides examples of different types of slopes through pictures and descriptions. It discusses zero slopes (horizontal), undefined slopes (vertical), positive slopes (increasing), negative slopes (decreasing), steeper slopes, and flatter slopes. Examples include a sunset, books on a shelf, a wire, buildings, a lamp post, grass, a rocket, mountains, stairs, a circus tent, people aligned downhill, and a glacier to illustrate the various slope categories.

Food Chain /Food Web

The document describes an activity on feeding relationships among living organisms in an ecosystem. It includes cards with activities identifying producers, consumers, and decomposers; illustrating food chains and webs; and assessing understanding of nutrient cycling and trophic levels. The goal is for students to observe and describe the feeding interrelationships between organisms through identification of producers, consumers, and decomposers and illustration of food chains and webs.

Slope (Algebra 2)

Students learn the definition of slope and calculate the slope of lines.
Students also learn to consider the slopes of parallel lines and perpendicular lines.

Slope

The document discusses slope and how to calculate it. It defines slope as the rate of change of a line and provides the formula slope=rise/run. It then explains how to find the slope of a line graph by picking two points and calculating rise over run. Finally, it demonstrates how to find the slope of a line given two points or from a table of x-y values using the same rise over run formula.

Science Intervention materials on science

This document is a science intervention material that discusses the concepts of force and work. It uses pictures, examples, and activities to teach students about different types of forces (contact vs. non-contact), what constitutes work, and how to calculate work using various formulas. The material guides students through examples of determining if a situation involves a contact or non-contact force, identifying whether work is being done in images, and solving word problems to calculate work done. It also includes review questions and activities to help students assess their understanding of these core science concepts.

Slope intercept intro

The document discusses the slope-intercept form of equations of lines. It explains that the slope-intercept form can be written as y = mx + b, where m is the slope and b is the y-intercept. The slope represents how fast the line rises or falls, and the y-intercept is where the line crosses the y-axis. Some examples of lines in slope-intercept form are worked out, identifying the slope and y-intercept in each case.

Action research for Strategic Intervention Materials

This document discusses a study that evaluated the effectiveness of using strategic intervention materials to improve 4th grade students' academic performance in science. It found that students who were taught using the strategic materials performed better on pre- and post-tests compared to students taught using traditional methods. The study developed science intervention materials aimed at reteaching least mastered concepts and skills. It assessed 330 4th grade students, with some sections taught traditionally and others using the new materials. Students using the materials showed greater gains in science performance compared to those taught traditionally.

Slope

Slope

Slopes in the real world url

Slopes in the real world url

2.2 linear equations and 2.3 Slope

2.2 linear equations and 2.3 Slope

Slope in real life!

Slope in real life!

Real life application of slope_Ajay_TD

Real life application of slope_Ajay_TD

Two point form Equation of a line

Two point form Equation of a line

Slopes in the real world

Slopes in the real world

Slope in the real world

Slope in the real world

Slopes in real life

Slopes in real life

Food Chain /Food Web

Food Chain /Food Web

Slope (Algebra 2)

Slope (Algebra 2)

Slope

Slope

Science Intervention materials on science

Science Intervention materials on science

Slope intercept intro

Slope intercept intro

Action research for Strategic Intervention Materials

Action research for Strategic Intervention Materials

Finding Slope 2009

The document provides instruction on calculating the slope of a line. It defines slope as the steepness of a line and discusses how to calculate it using rise over run when given two points on a graph, or using the slope formula when given the coordinates of two points. It provides examples of finding the slope in various contexts and situations, including when the slope is defined elsewhere in the question or when lines are horizontal or vertical.

5.1 Finding Slope

The student will learn to find the slope of a line given two points or a graph. Slope represents the steepness of a line and can be calculated using the formula of rise over run or by using the points in the slope formula. Horizontal lines have a slope of 0 and vertical lines have an undefined slope. The document provides examples of finding the slope of lines from graphs and points.

Finding slope

The document discusses slope and how to calculate it given points on a line or its graph. It provides examples of finding the slope between two points using the rise over run formula or slope formula. It explains that horizontal lines have a slope of 0 and vertical lines have undefined slope. It also gives an example of solving for an unknown value in one of the points when given the other point and slope.

FindingSlope.ppt

This document provides instruction on calculating and understanding slope. It defines slope as the steepness of a line and discusses how to calculate slope given two points on a line using the rise over run formula or the slope formula. It provides examples of finding the slope of lines from their graphs or given two points and discusses the slopes of horizontal and vertical lines.

local_media5416891530663583326.ppt

This document provides instruction on calculating and understanding slope. It defines slope as the steepness of a line and discusses how to calculate slope given two points on a line using the rise over run formula or the slope formula. It provides examples of finding the slope of lines from their graphs or given two points and discusses the slopes of horizontal and vertical lines.

Finding slope

This is a ppt for learning how to calculate the slope of a line within a line graph. This ppt works for about a 8th t 9th grade level.

8.3 Slope And Y Intercept

The document discusses slope and the slope-intercept form of linear equations. It defines slope as the ratio of the rise over the run between two points on a line. Slope can be calculated using two points or using the difference of the y-coordinates over the difference of the x-coordinates. Horizontal and vertical lines have special cases for slope calculations. The slope-intercept form is defined as y=mx+b, where m is the slope and b is the y-intercept. Using this form, lines can be graphed by plotting the y-intercept and using the slope to find the second point and draw the line.

3.5 Graphing Linear Equations in Slope-Intercept Form.pptx

This document discusses how to graph linear equations in slope-intercept form. It covers how to find the slope of a line using the slope formula, and how slope and y-intercept are used to graph linear equations. Students will learn to find the slope and y-intercept of an equation in slope-intercept form, plot the y-intercept, use the slope to find another point, and draw the line through the two points. Examples are provided to demonstrate these steps.

3.3g

This document discusses slopes of lines and their uses in transportation. It provides formulas and examples for calculating slopes from two points on a line. Key points made include:
1) The slope of a line is the ratio of its vertical rise to its horizontal run and indicates whether a line rises, falls, or is horizontal.
2) Parallel lines have the same slope, while perpendicular lines have slopes that multiply to -1.
3) Slope can be used to identify the rate of change in various contexts like increasing sales over time.

2.2 linear equations

The document discusses linear equations and slope. It covers plotting points on a coordinate plane, calculating slope using the rise over run formula, writing equations in slope-intercept form, and graphing lines by making a table or using the slope and y-intercept. Methods are provided for determining the equation of a line given two points, the slope and a point, or by finding values from a graph.

2.2 slope

1. The document discusses slope and rate of change, including how to calculate slope from two points on a line and how to interpret positive, negative, zero, and undefined slopes.
2. It provides examples of finding the slope of lines from graphs and points, and discusses how to identify parallel and perpendicular lines based on their slopes.
3. The key concepts are how to determine the steepness of a line from its slope, and that parallel lines have the same slope while perpendicular lines have slopes that are opposite reciprocals.

TechMathI - Rate of change and slope

The document contains information about rates of change, slope, and lines. It includes examples of calculating rates of change from tables of data and slope from ordered pairs using the slope formula. It discusses horizontal and vertical lines having slopes of 0 and undefined, and positive and negative slopes indicating the direction a line slants.

Linear equations part i

The document discusses linear equations and graphing lines. It covers plotting points, calculating slope, writing equations in slope-intercept form, and graphing lines by making a table or using the slope and y-intercept. Methods are presented for finding the equation of a line given two points, the slope and a point, or from a graph.

GraphingLinearEquations

The document discusses several methods for graphing linear equations:
1) Using a table and slope-intercept form to generate ordered pairs and plot points
2) Plotting the y-intercept and using slope to find another point with slope-intercept form
3) Plotting a starting point and using slope to find another with point-slope form
4) Finding the x-intercept and y-intercept by setting variables to 0 in standard form and connecting points

Coordinate Plane 2.ppt

This document provides an overview of linear equations and graphing lines. It covers basic coordinate plane information, plotting points, finding slopes, x- and y-intercepts, the slope-intercept form of a line, graphing lines using tables and slope-intercept form, and determining the equation of a line given different information like two points or a slope and point. The assignments section indicates students will apply these concepts to practice problems.

1555 linear equations

Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics

QUARTER-I-MOD-5-L-3-SLOPE-OF-A-LINE-given-two-points.pptx

The document discusses how to find the slope of a line by using two points on the line and the change in y over the change in x, or by analyzing the graph of the line, with examples of how to calculate slope for lines with positive, negative, zero, and undefined slopes. Learners should be able to illustrate and calculate the slope of a line given two points on it or its graph.

Linear equations part i

The document provides an overview of key concepts for linear equations including plotting points, finding slopes, graphing lines using the slope-intercept form, determining the equation of a line given two points, and assigning practice problems. Key steps include calculating slope as rise over run, writing equations in slope-intercept form, making a table of x-y values to graph lines, and using two points to find the equation of a line.

January 20, 2015

The document provides an agenda for today that includes:
- New topics on Khan Academy
- Warm-up/final exam preparation
- Using coordinate formulas
- Class work from last week
- Current class work
It then lists practice questions related to graphing, slopes of lines, writing equations of lines, finding intercepts, and using different forms of linear equations. The document provides instruction and examples for students to work on these math skills.

Geo 3.6&7 slope

Reveiws slope from algebra I, then shows how to find lines parallel and perpendicular to a given line through a given point.

Finding Slope 2009

Finding Slope 2009

5.1 Finding Slope

5.1 Finding Slope

Finding slope

Finding slope

FindingSlope.ppt

FindingSlope.ppt

local_media5416891530663583326.ppt

local_media5416891530663583326.ppt

Finding slope

Finding slope

8.3 Slope And Y Intercept

8.3 Slope And Y Intercept

3.5 Graphing Linear Equations in Slope-Intercept Form.pptx

3.5 Graphing Linear Equations in Slope-Intercept Form.pptx

3.3g

3.3g

2.2 linear equations

2.2 linear equations

2.2 slope

2.2 slope

TechMathI - Rate of change and slope

TechMathI - Rate of change and slope

Linear equations part i

Linear equations part i

GraphingLinearEquations

GraphingLinearEquations

Coordinate Plane 2.ppt

Coordinate Plane 2.ppt

1555 linear equations

1555 linear equations

QUARTER-I-MOD-5-L-3-SLOPE-OF-A-LINE-given-two-points.pptx

QUARTER-I-MOD-5-L-3-SLOPE-OF-A-LINE-given-two-points.pptx

Linear equations part i

Linear equations part i

January 20, 2015

January 20, 2015

Geo 3.6&7 slope

Geo 3.6&7 slope

Harnessing the Power of NLP and Knowledge Graphs for Opioid Research

Gursev Pirge, PhD
Senior Data Scientist - JohnSnowLabs

Leveraging the Graph for Clinical Trials and Standards

Katja Glaß
OpenStudyBuilder Community Manager - Katja Glaß Consulting
Marius Conjeaud
Principal Consultant - Neo4j

Christine's Product Research Presentation.pptx

How I do my Product Research

"NATO Hackathon Winner: AI-Powered Drug Search", Taras Kloba

This is a session that details how PostgreSQL's features and Azure AI Services can be effectively used to significantly enhance the search functionality in any application.
In this session, we'll share insights on how we used PostgreSQL to facilitate precise searches across multiple fields in our mobile application. The techniques include using LIKE and ILIKE operators and integrating a trigram-based search to handle potential misspellings, thereby increasing the search accuracy.
We'll also discuss how the azure_ai extension on PostgreSQL databases in Azure and Azure AI Services were utilized to create vectors from user input, a feature beneficial when users wish to find specific items based on text prompts. While our application's case study involves a drug search, the techniques and principles shared in this session can be adapted to improve search functionality in a wide range of applications. Join us to learn how PostgreSQL and Azure AI can be harnessed to enhance your application's search capability.

GlobalLogic Java Community Webinar #18 “How to Improve Web Application Perfor...

Під час доповіді відповімо на питання, навіщо потрібно підвищувати продуктивність аплікації і які є найефективніші способи для цього. А також поговоримо про те, що таке кеш, які його види бувають та, основне — як знайти performance bottleneck?
Відео та деталі заходу: https://bit.ly/45tILxj

Northern Engraving | Modern Metal Trim, Nameplates and Appliance Panels

What began over 115 years ago as a supplier of precision gauges to the automotive industry has evolved into being an industry leader in the manufacture of product branding, automotive cockpit trim and decorative appliance trim. Value-added services include in-house Design, Engineering, Program Management, Test Lab and Tool Shops.

Principle of conventional tomography-Bibash Shahi ppt..pptx

before the computed tomography, it had been widely used.

inQuba Webinar Mastering Customer Journey Management with Dr Graham Hill

HERE IS YOUR WEBINAR CONTENT! 'Mastering Customer Journey Management with Dr. Graham Hill'. We hope you find the webinar recording both insightful and enjoyable.
In this webinar, we explored essential aspects of Customer Journey Management and personalization. Here’s a summary of the key insights and topics discussed:
Key Takeaways:
Understanding the Customer Journey: Dr. Hill emphasized the importance of mapping and understanding the complete customer journey to identify touchpoints and opportunities for improvement.
Personalization Strategies: We discussed how to leverage data and insights to create personalized experiences that resonate with customers.
Technology Integration: Insights were shared on how inQuba’s advanced technology can streamline customer interactions and drive operational efficiency.

Northern Engraving | Nameplate Manufacturing Process - 2024

Manufacturing custom quality metal nameplates and badges involves several standard operations. Processes include sheet prep, lithography, screening, coating, punch press and inspection. All decoration is completed in the flat sheet with adhesive and tooling operations following. The possibilities for creating unique durable nameplates are endless. How will you create your brand identity? We can help!

A Deep Dive into ScyllaDB's Architecture

This talk will cover ScyllaDB Architecture from the cluster-level view and zoom in on data distribution and internal node architecture. In the process, we will learn the secret sauce used to get ScyllaDB's high availability and superior performance. We will also touch on the upcoming changes to ScyllaDB architecture, moving to strongly consistent metadata and tablets.

ScyllaDB Tablets: Rethinking Replication

ScyllaDB is making a major architecture shift. We’re moving from vNode replication to tablets – fragments of tables that are distributed independently, enabling dynamic data distribution and extreme elasticity. In this keynote, ScyllaDB co-founder and CTO Avi Kivity explains the reason for this shift, provides a look at the implementation and roadmap, and shares how this shift benefits ScyllaDB users.

Astute Business Solutions | Oracle Cloud Partner |

Your goto partner for Oracle Cloud, PeopleSoft, E-Business Suite, and Ellucian Banner. We are a firm specialized in managed services and consulting.

PRODUCT LISTING OPTIMIZATION PRESENTATION.pptx

How I do Keyword Research

Discover the Unseen: Tailored Recommendation of Unwatched Content

The session shares how JioCinema approaches ""watch discounting."" This capability ensures that if a user watched a certain amount of a show/movie, the platform no longer recommends that particular content to the user. Flawless operation of this feature promotes the discover of new content, improving the overall user experience.
JioCinema is an Indian over-the-top media streaming service owned by Viacom18.

GraphRAG for LifeSciences Hands-On with the Clinical Knowledge Graph

Tomaz Bratanic
Graph ML and GenAI Expert - Neo4j

QR Secure: A Hybrid Approach Using Machine Learning and Security Validation F...

QR Secure: A Hybrid Approach Using Machine Learning and Security Validation Functions to Prevent Interaction with Malicious QR Codes.
Aim of the Study: The goal of this research was to develop a robust hybrid approach for identifying malicious and insecure URLs derived from QR codes, ensuring safe interactions.
This is achieved through:
Machine Learning Model: Predicts the likelihood of a URL being malicious.
Security Validation Functions: Ensures the derived URL has a valid certificate and proper URL format.
This innovative blend of technology aims to enhance cybersecurity measures and protect users from potential threats hidden within QR codes 🖥 🔒
This study was my first introduction to using ML which has shown me the immense potential of ML in creating more secure digital environments!

AWS Certified Solutions Architect Associate (SAA-C03)

AWS Certified Solutions Architect Associate (SAA-C03)

JavaLand 2024: Application Development Green Masterplan

My presentation slides I used at JavaLand 2024

LF Energy Webinar: Carbon Data Specifications: Mechanisms to Improve Data Acc...

This LF Energy webinar took place June 20, 2024. It featured:
-Alex Thornton, LF Energy
-Hallie Cramer, Google
-Daniel Roesler, UtilityAPI
-Henry Richardson, WattTime
In response to the urgency and scale required to effectively address climate change, open source solutions offer significant potential for driving innovation and progress. Currently, there is a growing demand for standardization and interoperability in energy data and modeling. Open source standards and specifications within the energy sector can also alleviate challenges associated with data fragmentation, transparency, and accessibility. At the same time, it is crucial to consider privacy and security concerns throughout the development of open source platforms.
This webinar will delve into the motivations behind establishing LF Energy’s Carbon Data Specification Consortium. It will provide an overview of the draft specifications and the ongoing progress made by the respective working groups.
Three primary specifications will be discussed:
-Discovery and client registration, emphasizing transparent processes and secure and private access
-Customer data, centering around customer tariffs, bills, energy usage, and full consumption disclosure
-Power systems data, focusing on grid data, inclusive of transmission and distribution networks, generation, intergrid power flows, and market settlement data

Demystifying Knowledge Management through Storytelling

The Department of Veteran Affairs (VA) invited Taylor Paschal, Knowledge & Information Management Consultant at Enterprise Knowledge, to speak at a Knowledge Management Lunch and Learn hosted on June 12, 2024. All Office of Administration staff were invited to attend and received professional development credit for participating in the voluntary event.
The objectives of the Lunch and Learn presentation were to:
- Review what KM ‘is’ and ‘isn’t’
- Understand the value of KM and the benefits of engaging
- Define and reflect on your “what’s in it for me?”
- Share actionable ways you can participate in Knowledge - - Capture & Transfer

Harnessing the Power of NLP and Knowledge Graphs for Opioid Research

Harnessing the Power of NLP and Knowledge Graphs for Opioid Research

Leveraging the Graph for Clinical Trials and Standards

Leveraging the Graph for Clinical Trials and Standards

Christine's Product Research Presentation.pptx

Christine's Product Research Presentation.pptx

"NATO Hackathon Winner: AI-Powered Drug Search", Taras Kloba

"NATO Hackathon Winner: AI-Powered Drug Search", Taras Kloba

GlobalLogic Java Community Webinar #18 “How to Improve Web Application Perfor...

GlobalLogic Java Community Webinar #18 “How to Improve Web Application Perfor...

Northern Engraving | Modern Metal Trim, Nameplates and Appliance Panels

Northern Engraving | Modern Metal Trim, Nameplates and Appliance Panels

Principle of conventional tomography-Bibash Shahi ppt..pptx

Principle of conventional tomography-Bibash Shahi ppt..pptx

inQuba Webinar Mastering Customer Journey Management with Dr Graham Hill

inQuba Webinar Mastering Customer Journey Management with Dr Graham Hill

Northern Engraving | Nameplate Manufacturing Process - 2024

Northern Engraving | Nameplate Manufacturing Process - 2024

A Deep Dive into ScyllaDB's Architecture

A Deep Dive into ScyllaDB's Architecture

ScyllaDB Tablets: Rethinking Replication

ScyllaDB Tablets: Rethinking Replication

Astute Business Solutions | Oracle Cloud Partner |

Astute Business Solutions | Oracle Cloud Partner |

PRODUCT LISTING OPTIMIZATION PRESENTATION.pptx

PRODUCT LISTING OPTIMIZATION PRESENTATION.pptx

Discover the Unseen: Tailored Recommendation of Unwatched Content

Discover the Unseen: Tailored Recommendation of Unwatched Content

GraphRAG for LifeSciences Hands-On with the Clinical Knowledge Graph

GraphRAG for LifeSciences Hands-On with the Clinical Knowledge Graph

QR Secure: A Hybrid Approach Using Machine Learning and Security Validation F...

QR Secure: A Hybrid Approach Using Machine Learning and Security Validation F...

AWS Certified Solutions Architect Associate (SAA-C03)

AWS Certified Solutions Architect Associate (SAA-C03)

JavaLand 2024: Application Development Green Masterplan

JavaLand 2024: Application Development Green Masterplan

LF Energy Webinar: Carbon Data Specifications: Mechanisms to Improve Data Acc...

LF Energy Webinar: Carbon Data Specifications: Mechanisms to Improve Data Acc...

Demystifying Knowledge Management through Storytelling

Demystifying Knowledge Management through Storytelling

- 1. Objective The student will be able to: find the slope of a line given 2 points and a graph.
- 4. What does the 7% mean? 7% is the slope of the road. It means the road drops 7 feet vertically for every 100 feet horizontally. So, what is slope??? Slope is the steepness of a line. 7% 7 feet 100 feet
- 5. Finding Slope Given a Graph
- 6. When given the graph, it is easier to apply “ rise over run ”. 1) Determine the slope of the line.
- 7. Determine the slope of the line. Start with the lower point and count how much you rise and run to get to the other point! 6 3 run 3 6 = = rise Notice the slope is positive AND the line increases!
- 8. Determine the slope of the line. The line is decreasing (slope is negative). 2 -1 Find points on the graph. Use two of them and apply rise over run.
- 9. What is the slope of a horizontal line?
- 10. What is the slope of a vertical line?
- 11. Remember the word “VUXHOY” V ertical lines U ndefined slope X = number; This is the equation of the line. H orizontal lines O - zero is the slope Y = number; This is the equation of the line.
- 12. Types of Slope Positive Negative Zero Undefined or No Slope
- 13. Dude! You try one.
- 15. rise = 4 run = 5 m= rise run m= 4/5
- 16. Finding Slope Given 2 points
- 17. Find the slope of the line through the points (3,7) and (5, 19). x 1 y 1 x 2 y 2 m = 19 – 7 5 – 3 m = 12 2 m = 6
- 18. Find the slope of the line that passes through the points (-2, -2) and (4, 1). y 2 = 1 x 2 = 4 y 1 = -2 x 1 = -2
- 19. Find the slope of the line that goes through the points (-5, 3) and (2, 1).
- 20. The slope of a line that goes through the points (r, 6) and (4, 2) is 4. Find r. To solve this, plug the given information into the formula
- 21. To solve for r, simplify and write as a proportion. Cross multiply. 1(-4) = 4(4 – r)
- 22. Simplify and solve the equation. 1(-4) = 4(4 – r) -4 = 16 – 4r -16 -16 -20 = -4r -4 -4 5 = r The ordered pairs are (5, 6) and (4, 2)
- 23. Dude! You try one.
- 25. The End