Math1000 section1.10
•
0 likes•14 views
This document covers key concepts about lines in mathematics including: - Lines have a constant slope which can be calculated using the slope formula. - The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. - Lines are parallel if they have the same slope and perpendicular if their slopes are negative reciprocals. - Several examples are provided of finding the equation of a line given different conditions like two points or being parallel/perpendicular to another line.
Report
Share
Report
Share
Download to read offline
Recommended
Geometry unit 3.7
The document discusses slopes and equations of lines. It defines slope as rise over run and provides formulas for calculating slope given two points on a line. It explains that the slope-intercept form is y=mx+b and point-slope form is y-y1=m(x-x1). Examples are given of writing equations of lines given slope and a point or y-intercept. Horizontal and vertical lines are also addressed.
Geometry unit 3.8
This document provides examples and explanations about parallel and perpendicular lines. It defines parallel lines as lines in the same plane that do not intersect. Perpendicular lines intersect to form a 90 degree angle. Several examples show how to identify parallel and perpendicular lines based on their slopes. The document also demonstrates applications to geometry, such as showing when a figure like a parallelogram or right triangle is formed based on the relationships between line slopes.
Linear function and slopes of a line
This document provides an overview of linear functions and equations. It defines linear equations as having the standard form Ax + By = C, with examples and how to identify linear vs. nonlinear equations. Linear functions are defined as having the form f(x) = mx + b. The document discusses slope, x-intercepts, y-intercepts, and how to graph linear equations from these components. It also covers representing linear functions in slope-intercept form as y = mx + b, and point-slope form as y - y1 = m(x - x1).
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.
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.
Chapter 5 Using Intercepts
This document provides examples and explanations for finding the x-intercept and y-intercept of linear equations and using those intercepts to graph the line. It discusses interpreting the intercepts in real world contexts like time to complete a race or amount of items that can be purchased. Students are given examples of finding intercepts, graphing lines by plotting the intercept points, and word problems involving linear equations.
Dec 14
The document provides information about linear equations and their graphs. It defines linear equations and discusses how to write equations in slope-intercept form, point-slope form, and standard form. It also describes how to graph linear equations by plotting intercepts and using slope. Key topics covered include finding the slope between two points, determining if lines are parallel or perpendicular based on their slopes, and recognizing the intercepts on a graph of a linear equation in two variables.
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.
Recommended
Geometry unit 3.7
The document discusses slopes and equations of lines. It defines slope as rise over run and provides formulas for calculating slope given two points on a line. It explains that the slope-intercept form is y=mx+b and point-slope form is y-y1=m(x-x1). Examples are given of writing equations of lines given slope and a point or y-intercept. Horizontal and vertical lines are also addressed.
Geometry unit 3.8
This document provides examples and explanations about parallel and perpendicular lines. It defines parallel lines as lines in the same plane that do not intersect. Perpendicular lines intersect to form a 90 degree angle. Several examples show how to identify parallel and perpendicular lines based on their slopes. The document also demonstrates applications to geometry, such as showing when a figure like a parallelogram or right triangle is formed based on the relationships between line slopes.
Linear function and slopes of a line
This document provides an overview of linear functions and equations. It defines linear equations as having the standard form Ax + By = C, with examples and how to identify linear vs. nonlinear equations. Linear functions are defined as having the form f(x) = mx + b. The document discusses slope, x-intercepts, y-intercepts, and how to graph linear equations from these components. It also covers representing linear functions in slope-intercept form as y = mx + b, and point-slope form as y - y1 = m(x - x1).
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.
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.
Chapter 5 Using Intercepts
This document provides examples and explanations for finding the x-intercept and y-intercept of linear equations and using those intercepts to graph the line. It discusses interpreting the intercepts in real world contexts like time to complete a race or amount of items that can be purchased. Students are given examples of finding intercepts, graphing lines by plotting the intercept points, and word problems involving linear equations.
Dec 14
The document provides information about linear equations and their graphs. It defines linear equations and discusses how to write equations in slope-intercept form, point-slope form, and standard form. It also describes how to graph linear equations by plotting intercepts and using slope. Key topics covered include finding the slope between two points, determining if lines are parallel or perpendicular based on their slopes, and recognizing the intercepts on a graph of a linear equation in two variables.
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.
Chapter11
This document provides information about graphing linear equations. It begins by defining a linear equation as one whose solutions fall on a straight line. It explains how to identify if an equation is linear based on whether a constant change in the x-value corresponds to a constant change in the y-value. The document then gives examples of graphing equations and determining if they are linear based on whether their graphs form a straight line. It also discusses using tables to list the x and y-values of points that satisfy the equation.
February 18 2016
The document discusses various formulas used to represent lines in the coordinate plane, including:
- Slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
- Point-slope form: y – y1 = m(x – x1), where (x1, y1) is a known point on the line and m is the slope.
- Standard form: Ax + By = C, where A, B, and C are constants and A and B cannot both be 0.
It provides examples of writing equations of lines in different forms given information like the slope, a point, or the graph of the line. Converting between
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.
Systems of Inequalities
The document discusses graphing linear inequalities in two variables. It provides examples of graphing single inequalities, determining if ordered pairs are solutions, and graphing systems of inequalities by finding the intersection or union of the regions bounded by the inequalities. The key steps shown are using slope and y-intercept to graph lines representing inequalities and testing points to determine the shaded region.
Line and its slope
1. The document discusses various forms of linear equations including standard form (Ax + By = C), slope-intercept form (y = mx + b), and point-slope form (y - y1 = m(x - x1)).
2. It provides examples of transforming linear functions between these forms and discusses how to find the slope and y-intercept of a linear function from its graph.
3. The slope and direction of a linear function's graph is determined by whether its slope is positive or negative. A positive slope produces an upward rising line while a negative slope produces a downward falling line.
Slope formula
This document provides examples for calculating slope using the slope formula. It demonstrates how to find slope given two points on a line, from a graph or table, and from a linear equation. It also explains that slope represents rate of change and gives examples where slope describes things like plant growth rate or electricity cost increase over time.
Chapter 5 Identifying Linear Functions
- The document is a lesson on identifying and graphing linear functions. It provides examples of determining if a graph or set of ordered pairs represents a linear function based on whether the relationship is constant.
- It also discusses writing linear equations in standard form and using linear equations to graph the line by choosing values for the variable and plotting the corresponding points.
- Real-world examples are given to show restricting the domain and range based on the context and graphing linear functions as discrete points rather than a continuous line.
5.5 parallel perp lines
The document discusses point-slope form and writing linear equations. It provides examples of writing equations for lines that are parallel and perpendicular to given lines. Specifically, it explains that parallel lines have the same slope and different y-intercepts, while perpendicular lines have slopes that are negative reciprocals of each other. Examples are given of writing equations for parallel and perpendicular lines using point-slope form based on a given point and the slope of another line.
Chapter 5 Slopes of Parallel and Perpendicular Lines
This document provides a lesson on identifying and writing equations for parallel and perpendicular lines. It includes examples of identifying parallel lines based on their having the same slope. Perpendicular lines are defined as having slopes whose product is -1. The document also demonstrates how to write equations for lines parallel or perpendicular to a given line based on their point and slope. Examples are provided to illustrate finding slopes from graphs and using them to determine if lines are parallel or perpendicular.
Mathematics 8 Linear Functions
This document provides a module on linear functions. It defines linear functions as those that can be written in the form f(x) = mx + b, where m is the slope and b is the y-intercept. The module teaches how to determine if a function is linear, rewrite linear equations in slope-intercept form, and graph linear functions given various inputs like two points, x- and y-intercepts, slope and a point, or slope and y-intercept. Examples and practice problems are provided to help students learn to identify, write, and graph different types of linear functions.
Writing and Graphing slope intercept form
The document discusses graphing and writing equations in slope-intercept form (y=mx+b). It explains that the slope (m) is the coefficient and the y-intercept (b) is the constant. It provides examples of graphing lines by plotting the y-intercept and counting up/right by the slope. It also demonstrates writing equations given the slope and/or a point, including finding missing values like the y-intercept.
2 6 writing equations in point-slope form
This document provides information about writing equations of lines in point-slope form and discusses key concepts like:
- Point-slope form uses the slope (m) and a point (x1, y1) on the line to write the equation.
- It gives examples of writing equations of lines where the slope and point are given.
- It also covers writing equations of lines given two points by first calculating the slope and then using point-slope form.
- Finally, it discusses writing equations of lines parallel or perpendicular to given lines.
Rewriting Linear Equation from standard form to slope intercept form
This SIM was crafted to address the needs of learners with difficulty in rewriting linear equation from standard form into slope intercept form
Topic 8 (Writing Equations Of A Straight Lines)
The document provides information on properties of straight lines and methods to write equations of straight lines given different conditions. It also discusses solving systems of linear equations using different methods like graphing, substitution, elimination and Cramer's rule. Key points covered include writing equations in slope-intercept and standard form, finding slopes of parallel and perpendicular lines, and properties of consistent, inconsistent and dependent systems of linear equations.
11.3 slope of a line
This document discusses finding the slope of a line from two points or an equation. It provides the slope formula and explains how to calculate slope given two points on a line. It also discusses horizontal and vertical lines, which have slopes of 0 and undefined, respectively. The document shows how to find the slope of a line from its equation by solving for y and taking the coefficient of x. It concludes by explaining how to determine if two lines are parallel, perpendicular, or neither based on the equality or product of their slopes. Examples are provided to demonstrate these concepts.
Linear equation
1) The document discusses linear equations in slope-intercept (y=mx+b) and standard (ax+by=c) form. It provides examples of writing equations from graphs and vice versa.
2) Transformations of linear and quadratic equations are introduced, where changing coefficients or adding constants changes the graph by shifting it up/down or left/right.
3) Examples of graphing quadratic equations y=x^2 and transformations y=x^2+c and y=kx^2+c are shown and described.
Linear functions
The document discusses different forms and methods for graphing linear functions, including:
1) The standard, point-slope, and slope-intercept forms of linear equations.
2) Converting between these forms by solving for slope and y-intercept.
3) Graphing linear functions by finding the slope from two points using the point-slope form, making a table of x-y values, or finding the x- and y-intercepts.
4) Determining if two functions are parallel or perpendicular based on having equal or reciprocal slopes.
Chapter 5 The Slope Formula
The document is a lesson on calculating slope from various representations of lines, including two points, graphs, tables, and equations. It provides examples of finding the slope using different methods and interpreting what the slope represents in real-world contexts. Key methods covered are using the slope formula with two points, choosing points from graphs and tables, and finding the x- and y-intercepts of a line from its equation to then apply the slope formula.
Numerical method-Picards,Taylor and Curve Fitting.
Here i have given some topics which is related to numerical method and computing.I covered picards method, Taylors series method, Curve fitting of method of least square and fitting a non leaner curve.
3 5 graphing linear inequalities in two variables
This document discusses how to graph linear inequalities in two variables. It explains that linear inequalities contain x and y variables separated by an inequality symbol (<, >, ≤, ≥) and the boundary is a straight line. To check if a point is a solution, plug it into the inequality and see if it makes a true statement. Examples are provided of checking points for different inequalities. The document also discusses using solid vs dashed boundary lines depending on the inequality symbol and shading the correct side of the boundary line based on a test point. Methods for graphing simple one-variable inequalities and inequalities written in slope-intercept and standard form are presented along with examples.
58 slopes of lines
The document defines slope as the ratio of the rise (change in y-values) to the run (change in x-values) between two points on a line. It provides the exact formula for calculating slope as the change in y-values divided by the change in x-values. Examples are given to demonstrate calculating the slopes of various lines, with positive slopes for lines passing through Quadrants I and III and negative slopes for lines passing through Quadrants II and IV.
More Related Content
What's hot
Chapter11
This document provides information about graphing linear equations. It begins by defining a linear equation as one whose solutions fall on a straight line. It explains how to identify if an equation is linear based on whether a constant change in the x-value corresponds to a constant change in the y-value. The document then gives examples of graphing equations and determining if they are linear based on whether their graphs form a straight line. It also discusses using tables to list the x and y-values of points that satisfy the equation.
February 18 2016
The document discusses various formulas used to represent lines in the coordinate plane, including:
- Slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
- Point-slope form: y – y1 = m(x – x1), where (x1, y1) is a known point on the line and m is the slope.
- Standard form: Ax + By = C, where A, B, and C are constants and A and B cannot both be 0.
It provides examples of writing equations of lines in different forms given information like the slope, a point, or the graph of the line. Converting between
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.
Systems of Inequalities
The document discusses graphing linear inequalities in two variables. It provides examples of graphing single inequalities, determining if ordered pairs are solutions, and graphing systems of inequalities by finding the intersection or union of the regions bounded by the inequalities. The key steps shown are using slope and y-intercept to graph lines representing inequalities and testing points to determine the shaded region.
Line and its slope
1. The document discusses various forms of linear equations including standard form (Ax + By = C), slope-intercept form (y = mx + b), and point-slope form (y - y1 = m(x - x1)).
2. It provides examples of transforming linear functions between these forms and discusses how to find the slope and y-intercept of a linear function from its graph.
3. The slope and direction of a linear function's graph is determined by whether its slope is positive or negative. A positive slope produces an upward rising line while a negative slope produces a downward falling line.
Slope formula
This document provides examples for calculating slope using the slope formula. It demonstrates how to find slope given two points on a line, from a graph or table, and from a linear equation. It also explains that slope represents rate of change and gives examples where slope describes things like plant growth rate or electricity cost increase over time.
Chapter 5 Identifying Linear Functions
- The document is a lesson on identifying and graphing linear functions. It provides examples of determining if a graph or set of ordered pairs represents a linear function based on whether the relationship is constant.
- It also discusses writing linear equations in standard form and using linear equations to graph the line by choosing values for the variable and plotting the corresponding points.
- Real-world examples are given to show restricting the domain and range based on the context and graphing linear functions as discrete points rather than a continuous line.
5.5 parallel perp lines
The document discusses point-slope form and writing linear equations. It provides examples of writing equations for lines that are parallel and perpendicular to given lines. Specifically, it explains that parallel lines have the same slope and different y-intercepts, while perpendicular lines have slopes that are negative reciprocals of each other. Examples are given of writing equations for parallel and perpendicular lines using point-slope form based on a given point and the slope of another line.
Chapter 5 Slopes of Parallel and Perpendicular Lines
This document provides a lesson on identifying and writing equations for parallel and perpendicular lines. It includes examples of identifying parallel lines based on their having the same slope. Perpendicular lines are defined as having slopes whose product is -1. The document also demonstrates how to write equations for lines parallel or perpendicular to a given line based on their point and slope. Examples are provided to illustrate finding slopes from graphs and using them to determine if lines are parallel or perpendicular.
Mathematics 8 Linear Functions
This document provides a module on linear functions. It defines linear functions as those that can be written in the form f(x) = mx + b, where m is the slope and b is the y-intercept. The module teaches how to determine if a function is linear, rewrite linear equations in slope-intercept form, and graph linear functions given various inputs like two points, x- and y-intercepts, slope and a point, or slope and y-intercept. Examples and practice problems are provided to help students learn to identify, write, and graph different types of linear functions.
Writing and Graphing slope intercept form
The document discusses graphing and writing equations in slope-intercept form (y=mx+b). It explains that the slope (m) is the coefficient and the y-intercept (b) is the constant. It provides examples of graphing lines by plotting the y-intercept and counting up/right by the slope. It also demonstrates writing equations given the slope and/or a point, including finding missing values like the y-intercept.
2 6 writing equations in point-slope form
This document provides information about writing equations of lines in point-slope form and discusses key concepts like:
- Point-slope form uses the slope (m) and a point (x1, y1) on the line to write the equation.
- It gives examples of writing equations of lines where the slope and point are given.
- It also covers writing equations of lines given two points by first calculating the slope and then using point-slope form.
- Finally, it discusses writing equations of lines parallel or perpendicular to given lines.
Rewriting Linear Equation from standard form to slope intercept form
This SIM was crafted to address the needs of learners with difficulty in rewriting linear equation from standard form into slope intercept form
Topic 8 (Writing Equations Of A Straight Lines)
The document provides information on properties of straight lines and methods to write equations of straight lines given different conditions. It also discusses solving systems of linear equations using different methods like graphing, substitution, elimination and Cramer's rule. Key points covered include writing equations in slope-intercept and standard form, finding slopes of parallel and perpendicular lines, and properties of consistent, inconsistent and dependent systems of linear equations.
11.3 slope of a line
This document discusses finding the slope of a line from two points or an equation. It provides the slope formula and explains how to calculate slope given two points on a line. It also discusses horizontal and vertical lines, which have slopes of 0 and undefined, respectively. The document shows how to find the slope of a line from its equation by solving for y and taking the coefficient of x. It concludes by explaining how to determine if two lines are parallel, perpendicular, or neither based on the equality or product of their slopes. Examples are provided to demonstrate these concepts.
Linear equation
1) The document discusses linear equations in slope-intercept (y=mx+b) and standard (ax+by=c) form. It provides examples of writing equations from graphs and vice versa.
2) Transformations of linear and quadratic equations are introduced, where changing coefficients or adding constants changes the graph by shifting it up/down or left/right.
3) Examples of graphing quadratic equations y=x^2 and transformations y=x^2+c and y=kx^2+c are shown and described.
Linear functions
The document discusses different forms and methods for graphing linear functions, including:
1) The standard, point-slope, and slope-intercept forms of linear equations.
2) Converting between these forms by solving for slope and y-intercept.
3) Graphing linear functions by finding the slope from two points using the point-slope form, making a table of x-y values, or finding the x- and y-intercepts.
4) Determining if two functions are parallel or perpendicular based on having equal or reciprocal slopes.
Chapter 5 The Slope Formula
The document is a lesson on calculating slope from various representations of lines, including two points, graphs, tables, and equations. It provides examples of finding the slope using different methods and interpreting what the slope represents in real-world contexts. Key methods covered are using the slope formula with two points, choosing points from graphs and tables, and finding the x- and y-intercepts of a line from its equation to then apply the slope formula.
Numerical method-Picards,Taylor and Curve Fitting.
Here i have given some topics which is related to numerical method and computing.I covered picards method, Taylors series method, Curve fitting of method of least square and fitting a non leaner curve.
3 5 graphing linear inequalities in two variables
This document discusses how to graph linear inequalities in two variables. It explains that linear inequalities contain x and y variables separated by an inequality symbol (<, >, ≤, ≥) and the boundary is a straight line. To check if a point is a solution, plug it into the inequality and see if it makes a true statement. Examples are provided of checking points for different inequalities. The document also discusses using solid vs dashed boundary lines depending on the inequality symbol and shading the correct side of the boundary line based on a test point. Methods for graphing simple one-variable inequalities and inequalities written in slope-intercept and standard form are presented along with examples.
What's hot (20)
Chapter 5 Slopes of Parallel and Perpendicular Lines
Chapter 5 Slopes of Parallel and Perpendicular Lines
Rewriting Linear Equation from standard form to slope intercept form
Rewriting Linear Equation from standard form to slope intercept form
Numerical method-Picards,Taylor and Curve Fitting.
Numerical method-Picards,Taylor and Curve Fitting.
Similar to Math1000 section1.10
58 slopes of lines
The document defines slope as the ratio of the rise (change in y-values) to the run (change in x-values) between two points on a line. It provides the exact formula for calculating slope as the change in y-values divided by the change in x-values. Examples are given to demonstrate calculating the slopes of various lines, with positive slopes for lines passing through Quadrants I and III and negative slopes for lines passing through Quadrants II and IV.
Graphs linear equations and functions
hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
TechMathI - 3.1 - Lines in Space Day2
The document provides examples and problems related to finding slopes of lines, writing equations of lines parallel and perpendicular to given lines, finding the rate of change and slope from tables of values, and finding the point of intersection between two lines by setting their equations equal to each other. Students are prompted to work through additional practice problems involving these concepts.
4 more on slopes x
The document defines slope as the ratio of the "rise" over the "run" between two points on a line. Specifically, if the points are (x1, y1) and (x2, y2), then the slope m is equal to (y2 - y1) / (x2 - x1). It also discusses how to calculate the slope of a line given two points, and how the slope indicates whether a line rises or falls from left to right. Lines between the first and third quadrants have positive slopes, while lines between the second and fourth quadrants have negative slopes.
WRITING AND GRAPHING LINEAR EQUATIONS 1.pptx
The document discusses linear equations and graphing linear relationships. It defines key terms like slope, y-intercept, x-intercept, and provides examples of writing linear equations in slope-intercept form and point-slope form given certain information like a point and slope. It also discusses using tables and graphs to plot linear equations and find slopes from graphs or between two points. Real-world examples of linear relationships are provided as well.
1539 graphs linear equations and functions
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
Straight line
This document contains information about straight lines and their various forms of equations. It discusses the slope-intercept form, intercept form, two-point form and general form of a straight line. It provides examples of finding the equation of a line given certain conditions like two points, slope and intercept, perpendicular or parallel lines etc. There are also examples of problems involving finding slope, intercepts, perpendicular or parallel lines to a given line. The document contains the necessary formulas and steps to solve such problems.
37 more on slopes-x
The document defines slope as the ratio of the rise (change in y-values) to the run (change in x-values) between two points on a line. It provides the exact formula for calculating slope and gives examples of finding the slopes of various lines. Key points made include that horizontal lines have a slope of 0, vertical lines have an undefined slope, and lines through quadrants I and III have positive slopes while lines through quadrants II and IV have negative slopes.
identities1.2
The document discusses the concept of slope and how it is used to describe the steepness of a line. It defines slope as the ratio of the vertical change (rise) to the horizontal change (run) between two points on a line. Several forms of linear equations are presented, including point-slope form, slope-intercept form, and standard form. Relationships between parallel and perpendicular lines based on their slopes are also described. Examples are provided to demonstrate finding slopes, writing equations of lines, and determining if lines are parallel or perpendicular based on their slopes.
Algebra 2 Section 1-4
This document provides instruction on writing linear equations in slope-intercept form, point-slope form, and finding equations of lines parallel or perpendicular to given lines. It defines key vocabulary like slope, parallel, and perpendicular. Examples are worked through, like writing the equation of a line given its slope and a point, or finding the equation of a line perpendicular to another line passing through a given point. The problem set provided practices writing various linear equations.
Linear equations rev
This document discusses key concepts related to linear equations in two variables including:
1. Linear equations can be written in the form ax + by = c and are graphed as lines.
2. The slope of a line measures its steepness and is calculated using the slope formula.
3. Linear equations can be written in slope-intercept form y = mx + b or point-slope form y - y1 = m(x - x1) to graph the line.
4. Parallel lines have the same slope while perpendicular lines have slopes that are negative reciprocals.
TechMathI - Point slope form
The document provides examples and explanations of finding the rate of change and linear equations from tables of data points and given slopes and points. It includes examples of using the point-slope formula to write linear equations from a given point and slope, as well as examples of writing linear equations from two given points. Students are prompted to write linear equations for several examples.
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.
Linear equations 2-2 a graphing and x-y intercepts
The document provides information about graphing points and linear equations on the Cartesian coordinate plane. It defines key terms like ordered pairs, x- and y-intercepts, and quadrants. It explains how to graph linear equations by finding x- and y-intercepts or substituting values into the equation to find points. Horizontal and vertical lines are identified, with their equations using either a constant x or y value.
Mathematics.pdf
The document provides information about analytical geometry and straight lines. It defines key terms like slope, direction cosines, direction ratios, and equations of straight lines. Specifically:
1) Slope is the tangent of the angle between a line and the x-axis. Slope can be calculated as the rise over the run between two points.
2) There are three common forms for the equation of a straight line: slope-intercept form y=mx+c, slope-point form y-y1=m(x-x1), and intercept form x=k.
3) Direction cosines and ratios describe the orientation of a line in 3D space and are proportional to each other. The direction ratios
Math project
The document discusses key concepts about linear equations in two variables including:
1) It describes the Cartesian coordinate plane and how to plot points based on their x and y coordinates.
2) It explains how to find the slope, y-intercept, and x-intercept of a linear equation graphically and algebraically.
3) It provides examples of rewriting linear equations in slope-intercept form (y=mx+b) and using intercepts and slopes to graph lines on the coordinate plane.
1538 graphs & 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
คาบ 5 7
This document discusses linear equations in two variables. It defines linear equations and explains how to find the slope of a line using the slope formula. It presents the slope-intercept form and point-slope forms of linear equations and how to graph lines using these forms. It also discusses parallel and perpendicular lines based on the slopes of the lines.
1554 linear equations in two variables
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
Similar to Math1000 section1.10 (20)
Linear equations 2-2 a graphing and x-y intercepts
Linear equations 2-2 a graphing and x-y intercepts
More from StuartJones92
Math1000 section2.4
The document discusses the average rate of change of functions. It defines the average rate of change between two values x=a and x=b of a function f(x) as (f(b) - f(a)) / (b - a). This represents the slope of the secant line between the two points (a, f(a)) and (b, f(b)). Several examples are worked out calculating the average rate of change for different functions between given values of the variable. The document emphasizes that knowing how to work with fractions is important for solving these types of average rate of change problems.
Math1000 section2.6
The document discusses transformations of functions including translations, reflections, stretches, and compressions. It defines even and odd functions and provides examples of applying transformations to common parent functions like quadratic, square root, and absolute value functions. Examples are worked through to demonstrate how to obtain the graph of one function from another by applying different transformations.
Math1000 section2.3
The document contains instructions and solutions for multiple problems involving analyzing functions from their graphs. It asks the student to find specific function values, domains, ranges, intervals of increase and decrease, and local maxima and minima. The solutions provided include finding that f(-1) = 1, f(1) = 2, f(0) = 1, f(2) = 1, and the domain and range for one function. It also identifies the intervals over which another function is increasing and decreasing.
Math1000 section2.2
This document discusses graphing functions. It begins by introducing common functions like linear, quadratic, cubic, rational, absolute value, square root, and cube root functions. Examples of their graphs are shown. It then discusses using the vertical line test to determine if something is a function. Piecewise functions are introduced next along with steps for graphing them which include graphing each piece and indicating open and closed points. Examples of piecewise functions are given and discussed. The document concludes by noting T-tables can be used to graph but plotting each piece of piecewise functions is more accurate.
Math1000 section2.1
This document contains lecture notes from a Math 1000 class taught by Stuart Jones. It covers several topics related to functions, including definitions of functions, evaluating functions, piecewise functions, and the difference quotient. Key points covered include the definition of a function as a mapping from a domain to a range, evaluating functions at different inputs, how piecewise functions use different formulas in different intervals, and the formula for the difference quotient.
Math1000 section1.9
This document covers coordinate geometry and circle formulas taught in a Math 1000 course by Stuart Jones. It introduces the midpoint and distance formulas, showing examples of using them to find the midpoint between two points and the distance between two points. It then covers the standard equation of a circle, giving the formula (x - h)2 + (y - k)2 = r2 where (h, k) is the center and r is the radius. Several example problems are worked through applying this circle formula by finding the equation of a circle given its center and radius or given the endpoints of its diameter. The document emphasizes that students must memorize all the formulas for upcoming tests.
Math1000 section1.6
This document introduces complex numbers and how to perform basic operations with them. Complex numbers were created to account for negative numbers under a square root. The imaginary unit is i = √-1. Complex numbers are written in the form a + bi. To add or subtract complex numbers, simply add or subtract the real and imaginary parts separately. To multiply complex numbers, use FOIL and note that i^2 = -1. To divide complex numbers, multiply the numerator and denominator by the complex conjugate of the denominator. Complex numbers arise when solving quadratic equations using the quadratic formula.
Math1000 section1.5
This document provides an overview of different types of equations covered in a math class. It discusses linear equations, literal equations, quadratic equations that can be solved by factoring, completing the square, or the quadratic formula. Rational equations involve multiplying to eliminate denominators, while radical equations aim to isolate the radical term. Students are advised to memorize procedures and formulas and practice through homework problems.
Math1000 section1.4
This document discusses rational expressions and their domains. It explains that rational expressions involve a polynomial fraction with a polynomial in the numerator and denominator. The domain of a rational expression is where the denominator is not equal to 0. It provides examples of simplifying and performing operations on rational expressions such as multiplying, dividing, adding and subtracting them by using the same rules as fractions. These include cancelling common factors, multiplying/dividing by the reciprocal, and finding a common denominator.
Math1000 section1.3
This document provides an overview of algebraic expressions and polynomials from a Math 1000 course. It introduces polynomials as sums or differences of monomials, which are variables raised to exponents. Examples of adding, subtracting, and multiplying polynomials are shown. The key processes of factoring trinomials and special factoring formulas are also explained in detail. Factoring is emphasized as an important math skill.
Math1000 section1.2
This document discusses exponents and radicals in Math 1000 taught by Stuart Jones. It provides examples of evaluating expressions with exponents such as -24 and (-2)4. It also covers the rules for exponents such as adding when multiplying bases and subtracting when dividing bases. Radicals are also introduced along with examples of simplifying expressions with radicals. Rational exponents are defined as the nth root of x written as x1/n. Throughout, examples are worked through step-by-step to simplify expressions with exponents and radicals.
More from StuartJones92 (11)
Recently uploaded
Jemison, MacLaughlin, and Majumder "Broadening Pathways for Editors and Authors"
Jemison, MacLaughlin, and Majumder "Broadening Pathways for Editors and Authors"National Information Standards Organization (NISO)
This presentation was provided by Racquel Jemison, Ph.D., Christina MacLaughlin, Ph.D., and Paulomi Majumder. Ph.D., all of the American Chemical Society, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.Accounting for Restricted Grants When and How To Record Properly
In this webinar, member learned how to stay in compliance with generally accepted accounting principles (GAAP) for restricted grants.
Bossa N’ Roll Records by Ismael Vazquez.
Bossa N Roll Records presentation by Izzy Vazquez for Music Retail and Distribution class at Full Sail University
Geography as a Discipline Chapter 1 __ Class 11 Geography NCERT _ Class Notes...
Geography as discipline
Temple of Asclepius in Thrace. Excavation results
The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
Physical pharmaceutics notes for B.pharm students
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) Curriculum
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
NIPER 2024 MEMORY BASED QUESTIONS.ANSWERS TO NIPER 2024 QUESTIONS.NIPER JEE 2...
NIPER JEE PYQ
NIPER JEE QUESTIONS
MOST FREQUENTLY ASK QUESTIONS
NIPER MEMORY BASED QUWSTIONS
Benner "Expanding Pathways to Publishing Careers"
This presentation was provided by Rebecca Benner, Ph.D., of the American Society of Anesthesiologists, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.
How to Predict Vendor Bill Product in Odoo 17
This slide will guide us through the process of predicting vendor bill products based on previous purchases from the vendor in Odoo 17.
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...
Andreas Schleicher, Director of Education and Skills at the OECD presents at the launch of PISA 2022 Volume III - Creative Minds, Creative Schools on 18 June 2024.
Recently uploaded (20)
Jemison, MacLaughlin, and Majumder "Broadening Pathways for Editors and Authors"
Jemison, MacLaughlin, and Majumder "Broadening Pathways for Editors and Authors"
Accounting for Restricted Grants When and How To Record Properly
Accounting for Restricted Grants When and How To Record Properly
Geography as a Discipline Chapter 1 __ Class 11 Geography NCERT _ Class Notes...
Geography as a Discipline Chapter 1 __ Class 11 Geography NCERT _ Class Notes...
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) Curriculum
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) Curriculum
spot a liar (Haiqa 146).pptx Technical writhing and presentation skills
spot a liar (Haiqa 146).pptx Technical writhing and presentation skills
NIPER 2024 MEMORY BASED QUESTIONS.ANSWERS TO NIPER 2024 QUESTIONS.NIPER JEE 2...
NIPER 2024 MEMORY BASED QUESTIONS.ANSWERS TO NIPER 2024 QUESTIONS.NIPER JEE 2...
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...
Math1000 section1.10
- 1. Math 1000 Stuart Jones Section 1.10 Lines
- 2. Math 1000 Stuart Jones In this section, we will study the most basic graphed function - a line. A line is a graph that has a constant slope. To understand that, we need to define slope.
- 3. Math 1000 Stuart Jones Slope Formula Theorem The slope between any two points x1, y1) and x2, y2) is defined as y2 − y1 x2 − x1
- 4. Math 1000 Stuart Jones Find the slope between the points (4,6) and (3,5).
- 5. Math 1000 Stuart Jones Find the slope between the points (-4,7) and (2,13).
- 6. Math 1000 Stuart Jones The equation of a line is most often given via slope-intercept form. Slope-Intercept Form of a Line The slope-intercept form of a line is given by y = mx + b, where m is the slope, and b is the y-intercept. Note the x-intercept is where the function crosses the x-axis, and the y-intercept is where the function crosses the y-axis. To find the x-intercept, set y=0 and solve for x. To find the y-intercept, set x=0 and solve for y.
- 7. Math 1000 Stuart Jones Parallel & Perpendicular Lines A line is parallel to another line if their slopes are the same. A line is perpendicular to another line if their slopes are negative reciprocals of each other.
- 8. Math 1000 Stuart Jones Find the line with the information given: Passes through (4,5) and (0,0)
- 9. Math 1000 Stuart Jones Find the line with the information given: Passes through (4,5) and y-intercept y=-2
- 10. Math 1000 Stuart Jones Find the line with the information given: x-intercept of x=3 and parallel y = −2x − 4
- 11. Math 1000 Stuart Jones Find the line with the information given: Perpendicular to y = −x − 2, x-intercept of x=2
- 12. Math 1000 Stuart Jones Given the graph, give the line that is shown. −4 −3 −2 −1 1 2 3 4 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8
- 13. Math 1000 Stuart Jones Given the graph, give the line that is shown. −4 −3 −2 −1 1 2 3 4 −5 −4 −3 −2 −1 1 2 3
- 14. Math 1000 Stuart Jones Given the graph, give the line that is shown. −3 −2 −1 1 2 3 −6 −5 −4 −3 −2 −1 1 2
- 15. Math 1000 Stuart Jones The Bottom Line Make sure you know how to calculate slope and y=mx+b, and how to use it. The best way to find the equation of a line is to find two points and proceed from there.