5.5 Linear Equations Point Slope Form
•Download as PPT, PDF•
4 likes•2,484 views
The document discusses point-slope form for writing equations of lines. Point-slope form is defined as y - y1 = m(x - x1), where m is the slope and (x1, y1) is a given point on the line. Several examples are shown of writing equations of lines in point-slope form given the slope and a point, or two points to find the slope. Converting between point-slope, slope-intercept, and standard forms is also demonstrated.
Report
Share
Report
Share
![5.5 Writing Equations in Point-Slope Form ,[object Object],[object Object]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Recommended
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 Intercept Form
The document discusses key concepts for graphing linear equations including slope, slope-intercept form, and steps for graphing equations. It defines slope as the ratio of rise over run, or the vertical change over the horizontal change along a line. Slope-intercept form is defined as y=mx+b, where m is the slope and b is the y-intercept. Examples are given for finding the slope and y-intercept and writing equations in slope-intercept form.
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.
Chapter 5 Slope-Intercept Form
This document provides a lesson on writing and graphing linear equations in slope-intercept form. It begins with examples of finding the slope and y-intercept of lines and writing the equation in the form y = mx + b. Then it shows how to graph lines from their equations in slope-intercept form. Applications include writing cost functions and finding values. A quiz reviews writing equations from slopes and points and graphing lines from their equations.
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-
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.
Complex numbers And Quadratic Equations
This ppt is on the above mentioned topic with clear and interactive explainations and some examples too!
3 2 solving systems of equations (elimination method)
The document describes the elimination method for solving systems of equations. The key steps are:
1) Write both equations in standard form Ax + By = C
2) Determine which variable to eliminate using addition or subtraction
3) Solve the resulting equation for one variable
4) Substitute back into the original equation to solve for the other variable
5) Check that the solution satisfies both original equations
It provides examples showing how to set up and solve systems of equations using elimination, including word problems about supplementary angles and finding two numbers based on their sum and difference.
Recommended
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 Intercept Form
The document discusses key concepts for graphing linear equations including slope, slope-intercept form, and steps for graphing equations. It defines slope as the ratio of rise over run, or the vertical change over the horizontal change along a line. Slope-intercept form is defined as y=mx+b, where m is the slope and b is the y-intercept. Examples are given for finding the slope and y-intercept and writing equations in slope-intercept form.
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.
Chapter 5 Slope-Intercept Form
This document provides a lesson on writing and graphing linear equations in slope-intercept form. It begins with examples of finding the slope and y-intercept of lines and writing the equation in the form y = mx + b. Then it shows how to graph lines from their equations in slope-intercept form. Applications include writing cost functions and finding values. A quiz reviews writing equations from slopes and points and graphing lines from their equations.
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-
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.
Complex numbers And Quadratic Equations
This ppt is on the above mentioned topic with clear and interactive explainations and some examples too!
3 2 solving systems of equations (elimination method)
The document describes the elimination method for solving systems of equations. The key steps are:
1) Write both equations in standard form Ax + By = C
2) Determine which variable to eliminate using addition or subtraction
3) Solve the resulting equation for one variable
4) Substitute back into the original equation to solve for the other variable
5) Check that the solution satisfies both original equations
It provides examples showing how to set up and solve systems of equations using elimination, including word problems about supplementary angles and finding two numbers based on their sum and difference.
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.
Solving systems of linear equations by graphing lecture
This document discusses solving systems of linear equations by graphing. It defines a system of linear equations as two or more equations containing at least one variable. It explains that to solve a system by graphing, each equation should be written in slope-intercept form and then graphed on the same set of axes. The type of solution can be determined by examining the graphs - one solution if the lines intersect, no solution if the lines are parallel, or infinitely many solutions if the lines coincide. It provides examples to illustrate each type of solution and explains that the point of intersection or coinciding point(s) will be the solution(s) to plug back into the original system to check.
Lesson 9: The Product and Quotient Rule
These rules allow us to differentiate the product or quotient of functions whose derivatives are themselves known.
2.8 Absolute Value Functions
Absolute value functions have a V-shape and model situations involving distance or edges. The graph can be transformed by changing the slope (a), shifting the vertex horizontally (h), or shifting the vertex vertically (k). To graph, identify the vertex and axis of symmetry, then use the slope to sketch the right side and symmetry to complete the left. Writing the equation involves identifying the vertex (h, k) and slope (a).
Quadratic Formula Presentation
The document introduces two methods for solving quadratic equations - factoring and graphing. It provides examples of equations that cannot be solved using these methods. It then introduces the quadratic formula as the method to use for equations that cannot be factored or graphed easily. It walks through identifying the a, b, and c coefficients needed for the quadratic formula. It provides examples of using the formula and encourages practicing with a worksheet.
Equation of the line
1. The document discusses various forms of linear equations including general, two-point, intercept, point-slope, and slope-intercept forms.
2. It provides examples of writing equations in each form given specific information like two points, an x-intercept and y-intercept, a point and slope, or just a slope and y-intercept.
3. Guided practice problems are included for writing equations parallel or perpendicular to a given line.
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.
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.
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.
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.
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.
Solving Systems of Linear Inequalities
This document discusses solving systems of linear inequalities. It begins with examples of graphing two-inequality systems by shading the regions defined by each inequality boundary and finding the overlapping solution region. It also covers checking solutions by testing points. Applications include painting plates within cost and number limits and geometry shapes defined by inequalities. The document emphasizes representing "greater than" or "less than" situations with systems of inequalities and using graphing to find the solution region.
Quadratic equation
1) The document thanks Farooq Sir for providing a wonderful project to work on about quadratics.
2) It was a pleasure and wonderful experience for the author and their team to work on this project.
3) The author thanks all those who helped and motivated them to complete this project.
Graphs of Log functions
This document discusses different ways to represent functions:
(1) Algebraically using an equation like y=x+6
(2) Using a table of x-y pairs
(3) Graphically by plotting the relationship between x and y
It provides examples of each type of representation.
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.
Equations of a Line
This document provides instruction on writing equations of lines using different forms: slope-intercept, point-slope, two-point, and intercept forms. Examples are given for writing equations of lines when given characteristics like slope, points, or intercepts. The last section presents an application example of using line equations to determine if two sets of bones found in an excavation site are parallel.
Review Of Slope And The Slope Intercept Formula
The document reviews slope and the slope-intercept formula y=mx+b. It provides examples of finding the slope and y-intercept of various lines given their graphs or two points on the line. It also demonstrates how to write the equation of a line given two points and how to find the x- and y-intercepts of a line given its equation.
Solving quadratics by graphing
This document discusses how to solve quadratic equations by graphing. It explains that a quadratic equation is of the form y = ax^2 + bx + c, with a being the quadratic term, b the linear term, and c the constant. The number of real solutions is at most two: one solution, two solutions, or no solutions. Solutions are found by setting the equation equal to 0 and finding the x-intercepts of the graph. The graph of a quadratic is a parabola with the roots as the x-intercepts and the vertex as the maximum or minimum point. Quadratic equations can be graphed by making a table of x and y values to plot the parabola.
Slope and y intercept
This document discusses slope, y-intercept, and how to find and graph linear equations. It defines slope as the ratio that describes a line's tilt and explains how to calculate slope using rise over run between two points on a line. It also discusses how to find the y-intercept, and then use slope and y-intercept to write the equation of a line in y=mx+b form. Examples are provided for finding slope from tables of values and graphing linear equations on a coordinate plane.
Linear functions
This document defines and compares linear equations and linear functions. It explains that a linear equation involves one variable with the highest power being 1, while a linear function relates two variables with the highest power of one variable being 1. The document also defines domain as the set of input values and range as the set of output values. An example shows how to identify the domain and range from a set of ordered pairs for a linear function.
6 4 Point Slope Form
The document discusses point-slope form for writing linear equations. It provides examples of writing equations of lines given a point and slope, graphing lines from their point-slope form equations, and writing equations to model data in a table using point-slope form. Key steps covered are finding the slope between two points and using one point and the slope to write the equation in point-slope form.
Alg1 lesson 5-5
This document discusses different forms for writing equations of lines, including slope-intercept form, point-slope form, and standard form. It provides examples of writing equations in these forms given information like the slope, y-intercept, and a point that the line passes through. It also shows that the slope-intercept and point-slope forms represent the same line. The document asks the reader to write equations in point-slope and standard form given parts of the equation.
More Related Content
What's hot
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.
Solving systems of linear equations by graphing lecture
This document discusses solving systems of linear equations by graphing. It defines a system of linear equations as two or more equations containing at least one variable. It explains that to solve a system by graphing, each equation should be written in slope-intercept form and then graphed on the same set of axes. The type of solution can be determined by examining the graphs - one solution if the lines intersect, no solution if the lines are parallel, or infinitely many solutions if the lines coincide. It provides examples to illustrate each type of solution and explains that the point of intersection or coinciding point(s) will be the solution(s) to plug back into the original system to check.
Lesson 9: The Product and Quotient Rule
These rules allow us to differentiate the product or quotient of functions whose derivatives are themselves known.
2.8 Absolute Value Functions
Absolute value functions have a V-shape and model situations involving distance or edges. The graph can be transformed by changing the slope (a), shifting the vertex horizontally (h), or shifting the vertex vertically (k). To graph, identify the vertex and axis of symmetry, then use the slope to sketch the right side and symmetry to complete the left. Writing the equation involves identifying the vertex (h, k) and slope (a).
Quadratic Formula Presentation
The document introduces two methods for solving quadratic equations - factoring and graphing. It provides examples of equations that cannot be solved using these methods. It then introduces the quadratic formula as the method to use for equations that cannot be factored or graphed easily. It walks through identifying the a, b, and c coefficients needed for the quadratic formula. It provides examples of using the formula and encourages practicing with a worksheet.
Equation of the line
1. The document discusses various forms of linear equations including general, two-point, intercept, point-slope, and slope-intercept forms.
2. It provides examples of writing equations in each form given specific information like two points, an x-intercept and y-intercept, a point and slope, or just a slope and y-intercept.
3. Guided practice problems are included for writing equations parallel or perpendicular to a given line.
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.
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.
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.
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.
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.
Solving Systems of Linear Inequalities
This document discusses solving systems of linear inequalities. It begins with examples of graphing two-inequality systems by shading the regions defined by each inequality boundary and finding the overlapping solution region. It also covers checking solutions by testing points. Applications include painting plates within cost and number limits and geometry shapes defined by inequalities. The document emphasizes representing "greater than" or "less than" situations with systems of inequalities and using graphing to find the solution region.
Quadratic equation
1) The document thanks Farooq Sir for providing a wonderful project to work on about quadratics.
2) It was a pleasure and wonderful experience for the author and their team to work on this project.
3) The author thanks all those who helped and motivated them to complete this project.
Graphs of Log functions
This document discusses different ways to represent functions:
(1) Algebraically using an equation like y=x+6
(2) Using a table of x-y pairs
(3) Graphically by plotting the relationship between x and y
It provides examples of each type of representation.
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.
Equations of a Line
This document provides instruction on writing equations of lines using different forms: slope-intercept, point-slope, two-point, and intercept forms. Examples are given for writing equations of lines when given characteristics like slope, points, or intercepts. The last section presents an application example of using line equations to determine if two sets of bones found in an excavation site are parallel.
Review Of Slope And The Slope Intercept Formula
The document reviews slope and the slope-intercept formula y=mx+b. It provides examples of finding the slope and y-intercept of various lines given their graphs or two points on the line. It also demonstrates how to write the equation of a line given two points and how to find the x- and y-intercepts of a line given its equation.
Solving quadratics by graphing
This document discusses how to solve quadratic equations by graphing. It explains that a quadratic equation is of the form y = ax^2 + bx + c, with a being the quadratic term, b the linear term, and c the constant. The number of real solutions is at most two: one solution, two solutions, or no solutions. Solutions are found by setting the equation equal to 0 and finding the x-intercepts of the graph. The graph of a quadratic is a parabola with the roots as the x-intercepts and the vertex as the maximum or minimum point. Quadratic equations can be graphed by making a table of x and y values to plot the parabola.
Slope and y intercept
This document discusses slope, y-intercept, and how to find and graph linear equations. It defines slope as the ratio that describes a line's tilt and explains how to calculate slope using rise over run between two points on a line. It also discusses how to find the y-intercept, and then use slope and y-intercept to write the equation of a line in y=mx+b form. Examples are provided for finding slope from tables of values and graphing linear equations on a coordinate plane.
Linear functions
This document defines and compares linear equations and linear functions. It explains that a linear equation involves one variable with the highest power being 1, while a linear function relates two variables with the highest power of one variable being 1. The document also defines domain as the set of input values and range as the set of output values. An example shows how to identify the domain and range from a set of ordered pairs for a linear function.
What's hot (20)
Solving systems of linear equations by graphing lecture
Solving systems of linear equations by graphing lecture
Similar to 5.5 Linear Equations Point Slope Form
6 4 Point Slope Form
The document discusses point-slope form for writing linear equations. It provides examples of writing equations of lines given a point and slope, graphing lines from their point-slope form equations, and writing equations to model data in a table using point-slope form. Key steps covered are finding the slope between two points and using one point and the slope to write the equation in point-slope form.
Alg1 lesson 5-5
This document discusses different forms for writing equations of lines, including slope-intercept form, point-slope form, and standard form. It provides examples of writing equations in these forms given information like the slope, y-intercept, and a point that the line passes through. It also shows that the slope-intercept and point-slope forms represent the same line. The document asks the reader to write equations in point-slope and standard form given parts of the equation.
Module 4 topic 3 2nd
This document provides examples of writing equations of linear functions in different forms:
- Slope is defined as the rise over the run and is used to find equations in point-slope form.
- Vertical lines have undefined slope while horizontal lines have a zero slope.
- Examples show writing equations in point-slope, slope-intercept, and standard form by given a slope and point or through manipulation of variables.
- Standard form is defined as Ax + By = C.
Module 4 topic 3 similar problems
This document provides examples of writing equations of linear functions in slope-intercept form. It demonstrates finding the slope from two points, using the slope and a point to write the equation in point-slope form, writing equations for horizontal and vertical lines, writing equations from tables of values, and solving linear equations for y.
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.
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.
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.
2.4
This document discusses linear equations and their various forms. It covers finding the equation of a line given a point and slope using point-slope form, or given two points using the formula for slope and point-slope form. It also discusses writing equations in standard and slope-intercept form, finding intercepts to graph lines, and writing equations of lines parallel or perpendicular to given lines through a specified point. Examples are provided for each concept.
2.4
This document discusses linear equations and their various forms. It covers finding the equation of a line given a point and slope using point-slope form, or given two points using the formula for slope and point-slope form. It also discusses writing equations in standard and slope-intercept form, finding intercepts to graph lines, and writing equations of lines parallel or perpendicular to given lines through a specified point. Examples are provided for each concept.
Alg2 lesson 2.4
This document discusses finding the slope and y-intercept of a line given its equation in slope-intercept form. It provides examples of writing equations of lines given their slopes and points, or two points the line passes through. It also discusses writing the equation of a line perpendicular to another line given a point on the perpendicular line.
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.
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.
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.
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.
Alg2 lesson 2 4
This document discusses finding the equation of a line given different information. It covers:
1) Finding the slope (m=4/3) and y-intercept (b=-3) of the line 6x - 3y = 7 using the slope-intercept form of a line (y=mx+b).
2) Writing the equation of a line containing the point (1,2) with slope -1/2 using the point-slope form (y-y1=m(x-x1)).
3) Writing the equation of a line containing the points (-2,2) and (3,7) by finding the slope between the points and using the point-slope form
January 15, 2015
The document provides information and examples about coordinate planes and linear equations:
1) It reviews formulas for the standard form, slope-intercept form, and point-slope form of linear equations. Examples are given of writing equations from points and slopes using the point-slope form.
2) Classwork problems are assigned from section 2.11 and formulas/examples are provided to help with coordinate plane test preparation on writing linear equations from graphs.
3) Additional resources like Khan Academy and online guides are mentioned for further practice with coordinate plane and linear equation concepts.
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 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.
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
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.
Similar to 5.5 Linear Equations Point Slope Form (20)
Recently uploaded
How to Manage Your Lost Opportunities in Odoo 17 CRM
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...Nguyen Thanh Tu Collection
https://app.box.com/s/qhtvq32h4ybf9t49ku85x0n3xl4jhr15Walmart Business+ and Spark Good for Nonprofits.pdf
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...
Librarians are leading the way in creating future-ready citizens – now we need to update our spaces to match. In this session, attendees will get inspiration for transforming their library spaces. You’ll learn how to survey students and patrons, create a focus group, and use design thinking to brainstorm ideas for your space. We’ll discuss budget friendly ways to change your space as well as how to find funding. No matter where you’re at, you’ll find ideas for reimagining your space in this session.
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...National Information Standards Organization (NISO)
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.Main Java[All of the Base Concepts}.docx
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Aberdeen
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
How to Setup Warehouse & Location in Odoo 17 Inventory
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx
Iván Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
Chapter wise All Notes of First year Basic Civil Engineering.pptx
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
The Diamonds of 2023-2024 in the IGRA collection
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...Nguyen Thanh Tu Collection
https://app.box.com/s/y977uz6bpd3af4qsebv7r9b7s21935vdChapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptxMohd Adib Abd Muin, Senior Lecturer at Universiti Utara Malaysia
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Recently uploaded (20)
How to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRM
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
Walmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdf
Digital Artefact 1 - Tiny Home Environmental Design
Digital Artefact 1 - Tiny Home Environmental Design
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
How to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 Inventory
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
Chapter wise All Notes of First year Basic Civil Engineering.pptx
Chapter wise All Notes of First year Basic Civil Engineering.pptx
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
5.5 Linear Equations Point Slope Form
- 1. Do Now:
- 3. What we Know so far…. Slope Intercept Form Where m is the slope and b is the intercept
- 4. The New Stuff… Point- Slope Form Point- Slope form is: Where m is the slope and (x 1, y 1 ) is the given point
- 5. Point Slope Form Writing Equations of Lines
- 6. Write the equation of the line with slope 3 and passing through the point (1, 5). y – y 1 = m (x – x 1 ) Use Point-Slope Form
- 7. Write the equation of the line with slope ¾ and passing through the point (-5, 3). y – y 1 = m (x – x 1 ) Use Point-Slope Form
- 8. Write the equation of the line with slope -4/7 and passing through the point (2, -4). y – y 1 = m (x – x 1 )
- 9. Write the equation of the line passing through the points (-2, 6) and (3, -1). y – y 1 = m (x – x 1 ) Find the slope let's use (3, -1)
- 10. Write the equation of the line passing through the points (4, 3) and (6, 8). y – y 1 = m (x – x 1 ) Find the slope let's use (4, 3)
- 11. Write the equation of the line passing through the points (4, -3) and (-7, -1). y – y 1 = m (x – x 1 ) Find the slope let's use (4, -3)
- 12. Why does the point-slope form work? Find the slope between (x 1 , y 1 ) and (x, y). Reflexive propetry Point-Slope Form
- 13. Convert y = 3x + 2 to standard form. multiply both sides by -1
- 14. Convert to standard form. multiply both sides by -4
- 15. Convert to standard form. multiply both sides by 7
- 16. Write the equation of the line parallel the line 4x – 5y = 7 that passes through the point (-3, 7) What is the slope of the given line? y – y 1 = m (x – x 1 )
- 17. Write the equation of the line perpendicular the line 3x + 2y = 9 that passes through the point (2, 5) What is the slope of the given line? y – y 1 = m (x – x 1 )