Graphing lines
•Download as PPT, PDF•
0 likes•179 views
The document discusses graphing two lines with equations y = -3x and 6x + 2y = 4. It asks the reader to rewrite the equations in slope-intercept form, make a table of values, plot the points on a graph, and determine if the lines are parallel based on having the same slope and different y-intercepts. The lines are parallel because they have the same slope of -3 but different y-intercepts of 0 for y = -3x and 2 for 6x + 2y = 4.
Report
Share
Report
Share
Recommended
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.
Graphs of straight lines
This document discusses how to graph straight lines from tables of values and find equations of lines from their graphs. It provides examples of graphing the line y = 2x - 5 by plotting the points from its table of values on a coordinate plane and drawing the line through them. Exercises are included to graph additional lines from their equations in various forms and determine the equations of lines from their graphs. The concept of gradient and y-intercept is introduced for lines written in the form y = mx + b.
Investigation 8;06
1. The document discusses different families of lines graphed on a number plane. The red lines are parallel and have negative x terms in their equations. The blue lines are also parallel and have positive 2x terms.
2. Three lines intersect at the origin - the green line y=x, the blue line y=2x, and the red line y=-x. These lines all lack a constant term.
3. Investigating the graphs shows that lines with a negative x term slope down as x increases, while lines with a positive x term slope up. The constant b relates to where the line intercepts the y-axis, with higher b above the axis and lower b below it.
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.
Graphing a line using Slope-Intercept form
This document explains how to graph a line using the slope-intercept form of a line, y=mx+b, where m is the slope and b is the y-intercept. It gives the example of the line with slope -2/3 and y-intercept of 6, so the equation is y=-2/3x+6. To graph this line, you first plot the y-intercept point (0,6), then find a second point by moving down 2 units and right 3 units from the first point and connect the two points with a straight line with arrows on the ends.
Parallel and perpendicular lines
This document discusses parallel and perpendicular lines. Parallel lines have equal slopes and will never intersect. Perpendicular lines intersect at a right angle, and their slopes are negative reciprocals of each other. The document provides examples of determining if lines are parallel or perpendicular based on their slopes, graphing parallel and perpendicular lines, and finding equations of lines parallel or perpendicular to a given line through a specified point.
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.
5.6 Parallel & Perpendicular Lines
This document discusses parallel and perpendicular lines. It defines parallel lines as having the same slope and perpendicular lines as having slopes that are negative reciprocals of each other. It provides examples of finding equations of lines parallel or perpendicular to given lines using their slopes. It also covers finding the slope of a line perpendicular to a given line, writing equations in point-slope and slope-intercept form for lines perpendicular to other lines, and identifying slopes from equations written in various forms.
Recommended
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.
Graphs of straight lines
This document discusses how to graph straight lines from tables of values and find equations of lines from their graphs. It provides examples of graphing the line y = 2x - 5 by plotting the points from its table of values on a coordinate plane and drawing the line through them. Exercises are included to graph additional lines from their equations in various forms and determine the equations of lines from their graphs. The concept of gradient and y-intercept is introduced for lines written in the form y = mx + b.
Investigation 8;06
1. The document discusses different families of lines graphed on a number plane. The red lines are parallel and have negative x terms in their equations. The blue lines are also parallel and have positive 2x terms.
2. Three lines intersect at the origin - the green line y=x, the blue line y=2x, and the red line y=-x. These lines all lack a constant term.
3. Investigating the graphs shows that lines with a negative x term slope down as x increases, while lines with a positive x term slope up. The constant b relates to where the line intercepts the y-axis, with higher b above the axis and lower b below it.
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.
Graphing a line using Slope-Intercept form
This document explains how to graph a line using the slope-intercept form of a line, y=mx+b, where m is the slope and b is the y-intercept. It gives the example of the line with slope -2/3 and y-intercept of 6, so the equation is y=-2/3x+6. To graph this line, you first plot the y-intercept point (0,6), then find a second point by moving down 2 units and right 3 units from the first point and connect the two points with a straight line with arrows on the ends.
Parallel and perpendicular lines
This document discusses parallel and perpendicular lines. Parallel lines have equal slopes and will never intersect. Perpendicular lines intersect at a right angle, and their slopes are negative reciprocals of each other. The document provides examples of determining if lines are parallel or perpendicular based on their slopes, graphing parallel and perpendicular lines, and finding equations of lines parallel or perpendicular to a given line through a specified point.
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.
5.6 Parallel & Perpendicular Lines
This document discusses parallel and perpendicular lines. It defines parallel lines as having the same slope and perpendicular lines as having slopes that are negative reciprocals of each other. It provides examples of finding equations of lines parallel or perpendicular to given lines using their slopes. It also covers finding the slope of a line perpendicular to a given line, writing equations in point-slope and slope-intercept form for lines perpendicular to other lines, and identifying slopes from equations written in various forms.
Parallel and Perpendicular lines
Parallel lines have the same slope and never intersect. Two lines are parallel if their slopes are equal. The equation of a line parallel to a given line can be found using the point-slope formula with the same slope.
Perpendicular lines intersect at a right angle. Two lines are perpendicular if the product of their slopes is -1. The equation of a line perpendicular to a given line can be found using the point-slope formula with the slope of the perpendicular line being the negative reciprocal of the given line's slope. Examples are provided of finding if lines are parallel or perpendicular and constructing parallel and perpendicular lines through a given point.
8.3 Slope And Y Intercept
The document discusses slope and the slope-intercept form of linear equations. It defines slope as the ratio of the rise over the run between two points on a line. Slope can be calculated using two points or using the difference of the y-coordinates over the difference of the x-coordinates. Horizontal and vertical lines have special cases for slope calculations. The slope-intercept form is defined as y=mx+b, where m is the slope and b is the y-intercept. Using this form, lines can be graphed by plotting the y-intercept and using the slope to find the second point and draw the line.
2.2 slope
1. The document discusses slope and rate of change, including how to calculate slope from two points on a line and how to interpret positive, negative, zero, and undefined slopes.
2. It provides examples of finding the slope of lines from graphs and points, and discusses how to identify parallel and perpendicular lines based on their slopes.
3. The key concepts are how to determine the steepness of a line from its slope, and that parallel lines have the same slope while perpendicular lines have slopes that are opposite reciprocals.
Slopeinterceptform
Slope-intercept form is represented by the equation y=mx+b, where m is the slope and b is the y-intercept. There are three methods to find the slope: rise over run, change in y over change in x, and point-slope formula. The slope tells the rate of change, while the y-intercept is the initial value when x=0. To graph a line in slope-intercept form, you plot the y-intercept and then use the slope to trace successive points on the line by calculating the rise over run at each interval of x. Word problems can be modeled using this form by identifying the independent and dependent variables and finding their relationship through calculating slope from ordered pairs of known values.
Module Four Lesson 2 Remediation Notes - Slope intercept form
Slope-intercept form is represented by the equation y=mx+b, where m is the slope and b is the y-intercept. There are three methods to find the slope: rise over run, change in y over change in x, and point-slope formula. The slope tells the rate of change, while the y-intercept is the initial value when x=0. To graph a line in slope-intercept form, you plot the y-intercept and then use the slope to trace successive points on the line by calculating the rise over run at each interval. Word problems can be modeled using this form by identifying the independent and dependent variables and finding their relationship through calculating slope from ordered pairs of known values.
Graph of linear equations
This document discusses four methods for graphing linear equations on a coordinate plane:
1. Using any two points on the line.
2. Using the x-intercept and y-intercept.
3. Using the slope and y-intercept.
4. Using the slope and one known point.
Examples are provided to illustrate each method. Graphing linear equations is important for visualizing relationships between variables in real-life situations.
Linear inequalities in two variables
The document discusses linear inequalities in two variables and their graphical representations. It introduces the Cartesian coordinate system developed by Rene Descartes and its importance. It explains how to graph linear inequalities by first drawing the line as an equation, then determining whether to shade above or below the line based on whether a test point satisfies the inequality. Students are assigned to bring graphing paper, coloring materials, and a ruler to class on Monday to graph linear inequalities.
Parallel and Perpendicular Slopes lines
This document provides an overview of slope, parallel lines, and perpendicular lines. It defines key concepts such as slope, slope-intercept form, standard form, and point-slope form. It also discusses how to calculate slope and classify lines based on their slopes. The document notes that parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other. It provides examples of finding equations of parallel and perpendicular lines.
Graphing Linear Inequalities
- A linear inequality describes a region of the coordinate plane bounded by a line. Any point in the shaded region is a solution to the inequality.
- To graph a linear inequality, first solve it for y and graph the resulting equation as a line. Then, test a point not on the line to determine which side of the line to shade based on whether it satisfies the inequality.
- The line is drawn solid for ≤ or ≥ and dashed for < or >. Shading the correct side of the line indicates the full solution set of the inequality.
Slope power point grade 8
Slope measures the steepness of a line and is calculated as the rise over the run between two points on the line. Slope is defined as the change in the y-values divided by the change in the x-values and is represented by the letter m. A line's slope does not change based on the two points used in the calculation. Vertical lines have undefined slopes, horizontal lines have a slope of zero, and all other non-vertical lines have a constant slope that can be found graphically, using a table, or using two points on the line.
Parallel And Perpendicular Lines
This document discusses writing equations of parallel and perpendicular lines in slope-intercept form. It provides examples of finding the equations of lines parallel or perpendicular to given lines that pass through specified points. For parallel lines, the slopes are equal. For perpendicular lines, the slopes are negative reciprocals of each other.
Graphing Linear Equations Lesson
There are four main methods to graph linear equations:
1) Point plotting involves choosing x-values, substituting them into the equation to find corresponding y-values, and plotting the points.
2) Using intercepts finds the x and y-intercepts by substituting 0 for x or y and solving for the other variable.
3) The slope-intercept form finds the slope and y-intercept to graph the line.
4) A graphing calculator can be used by inputting the equation in slope-intercept form (y=mx + b) and evaluating it to graph the line.
7-1 Exploring Quadratic Functions
This document discusses key concepts about quadratic functions including that they form parabolas with an axis of symmetry, how to identify the a, b, and c coefficients, and that the vertex represents the minimum or maximum value depending on whether a is positive or negative. It also explains how to graph quadratic functions using a table of values on a calculator or by hand and how the width of the parabola relates to the value of a.
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.
w4 Linear Equation
This worksheet contains 12 math problems involving linear equations and graphs. The problems involve determining the equation of a line given its gradient and y-intercept, finding the gradient and y-intercept of a line given its equation, graphing lines based on data tables, finding equations of lines parallel or perpendicular to given lines, and identifying properties of pairs of lines.
Graphing Linear Equations Teacher Lecture
This document discusses how to graph linear equations in slope-intercept form. It defines key terms like slope, y-intercept, rise over run, and slope-intercept form. It explains that the slope is the rate of change between x and y and the y-intercept is the point where the line crosses the y-axis. The document provides examples of graphing different types of lines and reviews the steps to graph any equation in slope-intercept form.
Graphs of linear equation
This document discusses how to graph linear equations on a coordinate plane using different methods:
1) Using two points from the linear equation to plot and connect those points
2) Using the x-intercept and y-intercept, which are the points where the line crosses the x- and y-axes
3) Using the slope of the line and the y-intercept, where the slope is rise over run and the y-intercept is where the line crosses the y-axis
4) Using the slope of the line and one point from the linear equation
Real-world examples of linear equations include stock market trends and car payment plans.
Finding Point-Slope Equations
This document discusses how to write point-slope equations for lines given information like slope, points, and whether lines are parallel. It provides examples of finding slope from graphs or two points, using slopes and points to find the y-intercept and write the equation, and writing equations for parallel lines. Key steps include finding slope with "rise over run", using points and slope to solve for the y-intercept b and plug into y=mx+b, and parallel lines having the same slope.
6.6 Graphing Inequalities In Two Variables
This document discusses graphing linear inequalities in two variables. It provides definitions of key terms like half-plane and boundary. It also gives helpful hints for graphing different types of inequalities based on whether the sign is >, <, ≥, or ≤ and whether it involves just x and y or a slanted line. Examples are provided to demonstrate how to graph inequalities like y > 3, x - 2, y - 3x + 2, and an applied problem involving nickels and dimes. The key steps for graphing a linear inequality on the coordinate plane are outlined.
Graphing lines part 2 y = mx + b
This document discusses graphing lines using the slope-intercept form equation y=mx+b. It explains that m represents the slope and b represents the y-intercept. Examples are provided to demonstrate how to graph lines by identifying m and b values and plotting points. Students are guided in graphing several lines and then assigned independent practice graphing additional lines using the slope-intercept form.
5 4b Graphing Lines
This document provides instructions for graphing linear equations in slope-intercept form (y=mx+b). To graph: 1) Write the equation in y=mx+b form, 2) Plot the y-intercept, 3) Use the slope to determine if the line increases or decreases as you move from point to point, and 4) Draw the line connecting all points. Examples given are y=3x+1, y=x-5, y=7, and y=2x+3.
Geom 1point2
This document defines and describes basic geometric terms including points, lines, planes, and their intersections. It discusses concepts such as collinear points lying on the same line, coplanar points lying on the same plane, line segments consisting of endpoints and points between them, and opposite rays extending from the same point on opposite sides of another point. Examples are provided to illustrate these geometric concepts and relationships between points, lines, and planes.
More Related Content
What's hot
Parallel and Perpendicular lines
Parallel lines have the same slope and never intersect. Two lines are parallel if their slopes are equal. The equation of a line parallel to a given line can be found using the point-slope formula with the same slope.
Perpendicular lines intersect at a right angle. Two lines are perpendicular if the product of their slopes is -1. The equation of a line perpendicular to a given line can be found using the point-slope formula with the slope of the perpendicular line being the negative reciprocal of the given line's slope. Examples are provided of finding if lines are parallel or perpendicular and constructing parallel and perpendicular lines through a given point.
8.3 Slope And Y Intercept
The document discusses slope and the slope-intercept form of linear equations. It defines slope as the ratio of the rise over the run between two points on a line. Slope can be calculated using two points or using the difference of the y-coordinates over the difference of the x-coordinates. Horizontal and vertical lines have special cases for slope calculations. The slope-intercept form is defined as y=mx+b, where m is the slope and b is the y-intercept. Using this form, lines can be graphed by plotting the y-intercept and using the slope to find the second point and draw the line.
2.2 slope
1. The document discusses slope and rate of change, including how to calculate slope from two points on a line and how to interpret positive, negative, zero, and undefined slopes.
2. It provides examples of finding the slope of lines from graphs and points, and discusses how to identify parallel and perpendicular lines based on their slopes.
3. The key concepts are how to determine the steepness of a line from its slope, and that parallel lines have the same slope while perpendicular lines have slopes that are opposite reciprocals.
Slopeinterceptform
Slope-intercept form is represented by the equation y=mx+b, where m is the slope and b is the y-intercept. There are three methods to find the slope: rise over run, change in y over change in x, and point-slope formula. The slope tells the rate of change, while the y-intercept is the initial value when x=0. To graph a line in slope-intercept form, you plot the y-intercept and then use the slope to trace successive points on the line by calculating the rise over run at each interval of x. Word problems can be modeled using this form by identifying the independent and dependent variables and finding their relationship through calculating slope from ordered pairs of known values.
Module Four Lesson 2 Remediation Notes - Slope intercept form
Slope-intercept form is represented by the equation y=mx+b, where m is the slope and b is the y-intercept. There are three methods to find the slope: rise over run, change in y over change in x, and point-slope formula. The slope tells the rate of change, while the y-intercept is the initial value when x=0. To graph a line in slope-intercept form, you plot the y-intercept and then use the slope to trace successive points on the line by calculating the rise over run at each interval. Word problems can be modeled using this form by identifying the independent and dependent variables and finding their relationship through calculating slope from ordered pairs of known values.
Graph of linear equations
This document discusses four methods for graphing linear equations on a coordinate plane:
1. Using any two points on the line.
2. Using the x-intercept and y-intercept.
3. Using the slope and y-intercept.
4. Using the slope and one known point.
Examples are provided to illustrate each method. Graphing linear equations is important for visualizing relationships between variables in real-life situations.
Linear inequalities in two variables
The document discusses linear inequalities in two variables and their graphical representations. It introduces the Cartesian coordinate system developed by Rene Descartes and its importance. It explains how to graph linear inequalities by first drawing the line as an equation, then determining whether to shade above or below the line based on whether a test point satisfies the inequality. Students are assigned to bring graphing paper, coloring materials, and a ruler to class on Monday to graph linear inequalities.
Parallel and Perpendicular Slopes lines
This document provides an overview of slope, parallel lines, and perpendicular lines. It defines key concepts such as slope, slope-intercept form, standard form, and point-slope form. It also discusses how to calculate slope and classify lines based on their slopes. The document notes that parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other. It provides examples of finding equations of parallel and perpendicular lines.
Graphing Linear Inequalities
- A linear inequality describes a region of the coordinate plane bounded by a line. Any point in the shaded region is a solution to the inequality.
- To graph a linear inequality, first solve it for y and graph the resulting equation as a line. Then, test a point not on the line to determine which side of the line to shade based on whether it satisfies the inequality.
- The line is drawn solid for ≤ or ≥ and dashed for < or >. Shading the correct side of the line indicates the full solution set of the inequality.
Slope power point grade 8
Slope measures the steepness of a line and is calculated as the rise over the run between two points on the line. Slope is defined as the change in the y-values divided by the change in the x-values and is represented by the letter m. A line's slope does not change based on the two points used in the calculation. Vertical lines have undefined slopes, horizontal lines have a slope of zero, and all other non-vertical lines have a constant slope that can be found graphically, using a table, or using two points on the line.
Parallel And Perpendicular Lines
This document discusses writing equations of parallel and perpendicular lines in slope-intercept form. It provides examples of finding the equations of lines parallel or perpendicular to given lines that pass through specified points. For parallel lines, the slopes are equal. For perpendicular lines, the slopes are negative reciprocals of each other.
Graphing Linear Equations Lesson
There are four main methods to graph linear equations:
1) Point plotting involves choosing x-values, substituting them into the equation to find corresponding y-values, and plotting the points.
2) Using intercepts finds the x and y-intercepts by substituting 0 for x or y and solving for the other variable.
3) The slope-intercept form finds the slope and y-intercept to graph the line.
4) A graphing calculator can be used by inputting the equation in slope-intercept form (y=mx + b) and evaluating it to graph the line.
7-1 Exploring Quadratic Functions
This document discusses key concepts about quadratic functions including that they form parabolas with an axis of symmetry, how to identify the a, b, and c coefficients, and that the vertex represents the minimum or maximum value depending on whether a is positive or negative. It also explains how to graph quadratic functions using a table of values on a calculator or by hand and how the width of the parabola relates to the value of a.
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.
w4 Linear Equation
This worksheet contains 12 math problems involving linear equations and graphs. The problems involve determining the equation of a line given its gradient and y-intercept, finding the gradient and y-intercept of a line given its equation, graphing lines based on data tables, finding equations of lines parallel or perpendicular to given lines, and identifying properties of pairs of lines.
Graphing Linear Equations Teacher Lecture
This document discusses how to graph linear equations in slope-intercept form. It defines key terms like slope, y-intercept, rise over run, and slope-intercept form. It explains that the slope is the rate of change between x and y and the y-intercept is the point where the line crosses the y-axis. The document provides examples of graphing different types of lines and reviews the steps to graph any equation in slope-intercept form.
Graphs of linear equation
This document discusses how to graph linear equations on a coordinate plane using different methods:
1) Using two points from the linear equation to plot and connect those points
2) Using the x-intercept and y-intercept, which are the points where the line crosses the x- and y-axes
3) Using the slope of the line and the y-intercept, where the slope is rise over run and the y-intercept is where the line crosses the y-axis
4) Using the slope of the line and one point from the linear equation
Real-world examples of linear equations include stock market trends and car payment plans.
Finding Point-Slope Equations
This document discusses how to write point-slope equations for lines given information like slope, points, and whether lines are parallel. It provides examples of finding slope from graphs or two points, using slopes and points to find the y-intercept and write the equation, and writing equations for parallel lines. Key steps include finding slope with "rise over run", using points and slope to solve for the y-intercept b and plug into y=mx+b, and parallel lines having the same slope.
6.6 Graphing Inequalities In Two Variables
This document discusses graphing linear inequalities in two variables. It provides definitions of key terms like half-plane and boundary. It also gives helpful hints for graphing different types of inequalities based on whether the sign is >, <, ≥, or ≤ and whether it involves just x and y or a slanted line. Examples are provided to demonstrate how to graph inequalities like y > 3, x - 2, y - 3x + 2, and an applied problem involving nickels and dimes. The key steps for graphing a linear inequality on the coordinate plane are outlined.
What's hot (19)
Module Four Lesson 2 Remediation Notes - Slope intercept form
Module Four Lesson 2 Remediation Notes - Slope intercept form
Viewers also liked
Graphing lines part 2 y = mx + b
This document discusses graphing lines using the slope-intercept form equation y=mx+b. It explains that m represents the slope and b represents the y-intercept. Examples are provided to demonstrate how to graph lines by identifying m and b values and plotting points. Students are guided in graphing several lines and then assigned independent practice graphing additional lines using the slope-intercept form.
5 4b Graphing Lines
This document provides instructions for graphing linear equations in slope-intercept form (y=mx+b). To graph: 1) Write the equation in y=mx+b form, 2) Plot the y-intercept, 3) Use the slope to determine if the line increases or decreases as you move from point to point, and 4) Draw the line connecting all points. Examples given are y=3x+1, y=x-5, y=7, and y=2x+3.
Geom 1point2
This document defines and describes basic geometric terms including points, lines, planes, and their intersections. It discusses concepts such as collinear points lying on the same line, coplanar points lying on the same plane, line segments consisting of endpoints and points between them, and opposite rays extending from the same point on opposite sides of another point. Examples are provided to illustrate these geometric concepts and relationships between points, lines, and planes.
GraphingLinearEquations
The document discusses several methods for graphing linear equations:
1) Using a table and slope-intercept form to generate ordered pairs and plot points
2) Plotting the y-intercept and using slope to find another point with slope-intercept form
3) Plotting a starting point and using slope to find another with point-slope form
4) Finding the x-intercept and y-intercept by setting variables to 0 in standard form and connecting points
March 8 Graphing Slope Intercept
The document discusses using the slope-intercept method to graph lines. It explains that the slope-intercept method involves finding a point on the line, such as the y-intercept, and using the slope to find another point. It then works through examples of graphing lines using this method, showing how to identify the slope and y-intercept from equations in slope-intercept form or standard form.
Day 15 graphing lines stations
The document is about graphing lines stations for a math class. It includes instructions and examples for 4 stations where students graph lines from given equations and write the equation of a line from its graph. The stations provide practice identifying the equations of lines from graphs and plotting lines on graph paper from equations. There is also an activity where students create and trade linear equations to graph each other's lines.
Solving Systems by Graphing
Systems of lines can relate in three ways: they can cross at a single point, be parallel, or be the same line. Parallel lines have no solution since they never intersect. The same line has an infinite number of solutions since all points satisfy both equations. Lines that cross at a single point have a unique solution that can be found by putting the point of intersection into both equations.
Graphing lines using slopeintercept
This document provides information about graphing lines using slope-intercept form. It defines slope-intercept form as y=mx+b, where m is the slope and b is the y-intercept. It shows how to find the slope and y-intercept from linear equations in various forms and how to write equations in slope-intercept form. It also demonstrates how to graph lines by plotting points using the slope and y-intercept. Key steps for graphing include finding the slope and y-intercept, plotting the y-intercept, using the slope to determine other points, and drawing the line through the points. The document also discusses parallel lines as those with the same slope.
Graphing Performance Task
This document provides an overview of resources for teaching graphing to middle school students. It discusses the importance of graphing and using technology and visuals to help students understand the concept. Various websites, blogs, videos, apps and interactive activities are presented that teachers can use to incorporate graphing in their classroom, including real-world examples to demonstrate key concepts. Both teachers and students can access these online resources to support learning about graphing.
Graphing lines pp
This document provides instruction on graphing lines. It covers graphing horizontal and vertical lines given their equations, as well as graphing lines given two points, one point and a slope, or one point and an undefined slope. Examples are provided for each case, with checkpoints asking students to graph lines from given information. The document concludes with an individual practice section asking students to graph 5 lines from given information.
CST 504 Graphing Inequalities
This document provides instructions for graphing inequalities on a coordinate plane. It begins by graphing examples of inequalities on a number line and plane. It then explains how to graph linear inequalities by writing them as equations, making a table of x-y values, plotting the points, and drawing the boundary line. Examples are provided of graphing inequalities in slope-intercept form such as y ≥ -3x + 2. The document also covers testing points, determining whether to shade above or below the line, and applying the process to graph more complex inequalities like 3x - 4y > 12. It concludes with an example of using inequalities to model real-world constraints and find maximum/minimum values through optimization
5 1c Graphing lines from a point and slope
Given a point and slope, this document provides instructions for graphing the line through that point with the given slope. It explains that you should plot the point, determine if the slope is positive, negative, zero, or undefined, then use the slope to move up/down and over from the point to draw the line. It also notes that if the slope is a whole number, it should be converted to a ratio, and provides examples of graphing lines from different points with various slopes.
Lesson 3 angle between two intersecting lines
The document discusses how to find the angle between two lines that intersect. It provides examples of finding the angle between lines defined by two points each and discusses how to determine the angle when additional information is given, such as one line making a 45 degree angle and one having a specific slope. It also gives an example of finding the interior angles of a triangle given the coordinates of its vertices.
111020 analytic geometry
The document discusses the importance of understanding geometric concepts through real-world objects and examples, rather than just focusing on procedures and calculations. It provides several examples of using lines, planes, and shapes within objects to help students visualize and comprehend geometric relationships over just using equations and finding points of intersection. The examples include discussing lines and planes within cubes, pyramids, roofs and other objects. The goal is to help students progress from visualizing real situations, to drawing representations, to then expressing things analytically to build conceptual understanding.
Postulates (Geometry 1_3)
This document discusses geometry postulates, which are basic statements accepted as true without proof. It provides four postulates:
1) Two points determine a unique line.
2) If two lines intersect, their intersection is a point.
3) Three noncollinear points determine a unique plane.
4) If two planes intersect, their intersection is a line.
The document then provides examples of applying these postulates to identify lines and planes given certain points.
The Coordinate Plane (Geometry 2_4)
The document discusses the coordinate plane and graphing ordered pairs of numbers on it. It defines key terms like the x-axis, y-axis, origin, quadrants, and ordered pairs. Each ordered pair corresponds to exactly one point on the coordinate plane. Graphing an ordered pair involves locating the point based on its x and y coordinates.
Math14 lesson 5
The document discusses different types of equations that can represent straight lines in a plane, including point-slope form, two-point form, slope-intercept form, and normal form. It provides examples of writing the equation of a line given characteristics like two points, slope and intercept, or being parallel/perpendicular to another line. The document also covers topics like finding the distance from a point to a line and the equations of angle bisectors.
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.
Line And Angle Relationships
This document defines and explains different types of angles and angle relationships, including:
- Acute, right, obtuse, and straight angles
- Parallel and perpendicular lines
- Vertical, corresponding, alternate interior, alternate exterior, and consecutive interior angles
- Complementary, supplementary, and adjacent angles
Worked examples are provided to demonstrate finding missing angle measures using properties of these angles and angle relationships.
Problems in-plane-geometry-Sharygin
This document is the preface and table of contents for a book titled "Problems in Plane Geometry" that contains over 600 geometry problems divided into two sections. The preface provides background on the book, noting it contains both simple and more challenging problems, with detailed solutions. The table of contents outlines the chapters and topics covered, including fundamental theorems, loci of points, triangles, circles, polygons, and inequalities. The book is a collection of puzzles aimed at demonstrating elegant techniques in elementary geometry.
Viewers also liked (20)
Similar to Graphing lines
Week 1 discussion : Systems of linear equations
Read the explanation in each lesson carefully, then study the examples given before
doing the exercises.
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.
Graphing, Slope, And Special Lines
This document discusses graphing linear equations and determining slope. It provides examples of graphing lines with given equations like y = 2x - 4 and finding the slopes between points. Special lines like horizontal and vertical lines are examined, where horizontal lines have a slope of 0 and vertical lines are undefined. Pairs of lines are graphed and observed to have the same or opposite slopes based on their equations. In conclusion, the slope is important in graphing linear equations and representing the steepness of inclined lines.
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.
4 6 equations of lines
The document discusses equations of lines. It introduces the linear equation y = 2x - 1 and shows how to graph it by substituting values for x and finding the corresponding y-values. This forms the line's points (ordered pairs). It explains that a linear equation can be written in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. It provides examples of writing equations from their graphs in slope-intercept form and graphing lines from equations written in this form by using the slope and y-intercept. Finally, it gives examples of writing equations of lines parallel or perpendicular to given lines that pass through a given point.
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
Linear Equations in Two Variables.pptx
The document discusses linear equations in two variables. It will cover writing linear equations in standard and slope-intercept form, graphing linear equations using two points, intercepts and slope/point, and describing graphs by their intercepts and slope. Key topics include defining the standard form as Ax + By = C, rewriting equations between the two forms, using two points, x-intercept, y-intercept or slope/point to graph, and describing graphs by their slope and intercepts.
Module 1 plane coordinate geometry
The document provides information about module 1 on plane coordinate geometry. It will explain the relationship between lines on a plane, including intersecting, parallel and perpendicular lines. It will also cover determining the point of intersection between two lines algebraically and identifying if lines are parallel, perpendicular or neither based on their equations. Examples are provided to find the intersection of lines and to determine if lines are parallel, perpendicular or intersecting without graphing.
Skill36 parallels and perpendiculars
This lesson helps you decide whether two lines are parallel or perpendicular or neither (just intersecting lines).
Writing linear equations KG Math Middle School
The document provides information about graphing and writing linear equations in slope-intercept form (y=mx+b). It defines slope and y-intercept, and explains how to graph lines by using the slope and y-intercept. It also demonstrates how to write an equation of a line when given the slope and y-intercept, a point and the slope, or two points. Key steps include finding the slope using the formula (m=(y2-y1)/(x2-x1)), setting up and solving equations to find the y-intercept, and plugging the slope and y-intercept into the slope-intercept form to write the equation.
Maths
This document discusses linear equations in two variables. It defines linear equations in two variables as equations of the form ax + by = c, where a, b, and c are real numbers and a and b are not both zero. It explains that the graph of any linear equation in two variables is a straight line. It also categorizes different types of systems of linear equations based on the relationship between the lines: intersecting lines have a unique solution; coincident lines have an infinite number of solutions; and parallel lines have no solution. Methods for solving systems of linear equations like substitution, elimination, and graphing are also covered.
chapter1_part2.pdf
1. This document discusses linear equations, slope, graphing lines, writing equations in slope-intercept form, and solving systems of linear equations.
2. Key concepts explained include slope as rise over run, the different forms of writing a linear equation, finding the x- and y-intercepts, and using two points to write the equation of a line in slope-intercept form.
3. Examples are provided to demonstrate how to graph lines based on their equations in different forms, find intercepts, write equations from two points, and solve systems of linear equations.
January 9, 2014
The document provides information about linear equations and graphs:
- It defines the slope formula for finding the slope between two points on a line.
- It explains the slope-intercept form of a linear equation where y=mx+b, with m being the slope and b being the y-intercept.
- It gives examples of writing equations in slope-intercept form and graphing lines from their equations.
- It discusses other forms like point-slope form and how to write equations of lines given characteristics like a point and slope.
- It defines parallel and perpendicular lines based on their slopes being equal or negative reciprocals, respectively.
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 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.
2.2 linear equations
The document discusses linear equations and slope. It covers plotting points on a coordinate plane, calculating slope using the rise over run formula, writing equations in slope-intercept form, and graphing lines by making a table or using the slope and y-intercept. Methods are provided for determining the equation of a line given two points, the slope and a point, or by finding values from a graph.
12 LINEAR EQUATIONS.ppt
This document discusses writing equations of lines given different information. It explains how to write the equation of a line given the slope and y-intercept, slope and a point, or two points. It also covers determining if two lines are perpendicular or parallel based on comparing their slopes. Examples are provided for writing equations of lines and determining if lines are perpendicular or parallel.
คาบ2 2
The document provides instructions for writing and graphing linear equations in slope-intercept form (y = mx + b). It defines key terms like slope (m), y-intercept (b), and parallel lines. Examples are given for writing equations from slope and y-intercept, graphing lines on a coordinate plane, and determining if two lines are parallel based on having the same slope. Key steps are outlined for graphing a line passing through a given point with a given slope.
Ml lesson 4 7
The document discusses graphing lines using slope-intercept form. It provides examples of finding the slope and y-intercept of lines given their equations or points on the line. It also gives examples of writing equations of lines given the slope and y-intercept or a graph of the line. Finally, it discusses parallel lines and how they have the same slope.
Similar to Graphing lines (20)
Recently uploaded
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...Nguyen Thanh Tu Collection
https://app.box.com/s/tacvl9ekroe9hqupdnjruiypvm9rdaneBeyond 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
Constructing Your Course Container for Effective Communication
Communicating effectively and consistently with students can help them feel at ease during their learning experience and provide the instructor with a communication trail to track the course's progress. This workshop will take you through constructing an engaging course container to facilitate effective communication.
Advanced Java[Extra Concepts, Not Difficult].docx
This is part 2 of my Java Learning Journey. This contains Hashing, ArrayList, LinkedList, Date and Time Classes, Calendar Class and more.
Wound healing PPT
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Bed Making ( Introduction, Purpose, Types, Articles, Scientific principles, N...
Topic : Bed making
Subject : Nursing Foundation
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
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/qhtvq32h4ybf9t49ku85x0n3xl4jhr15How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience Wahiba Chair Training & Consulting
Wahiba Chair's Talk at the 2024 Learning Ideas Conference. 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).
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
-------------------------------------------------------------------------------
Find out more about ISO training and certification services
Training: ISO/IEC 27001 Information Security Management System - EN | PECB
ISO/IEC 42001 Artificial Intelligence Management System - EN | PECB
General Data Protection Regulation (GDPR) - Training Courses - EN | PECB
Webinars: https://pecb.com/webinars
Article: https://pecb.com/article
-------------------------------------------------------------------------------
For more information about PECB:
Website: https://pecb.com/
LinkedIn: https://www.linkedin.com/company/pecb/
Facebook: https://www.facebook.com/PECBInternational/
Slideshare: http://www.slideshare.net/PECBCERTIFICATION
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.
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.
Recently uploaded (20)
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx
Constructing Your Course Container for Effective Communication
Constructing Your Course Container for Effective Communication
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Bed Making ( Introduction, Purpose, Types, Articles, Scientific principles, N...
Bed Making ( Introduction, Purpose, Types, Articles, Scientific principles, N...
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 ...
How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) Curriculum
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) Curriculum
Graphing lines
- 1. Graphing Two Lines Are the lines parallel? Do lines intersect at a point?
- 2. Graph Two Lines Graph the two lines. Are they parallel? Why or why not.
- 3. Do we need to do anything to y = -3x? Step 1: Rewrite both equations in slope-intercept form. Reminder, slope-intercept form: y = mx + b. Do you notice anything about the slopes of the two equations? No, y = -3x is already in slope-intercept form. The two lines have the same slope, -3.
- 6. Are these lines parallel?
Editor's Notes
- Other methods which we will discuss in class. Check what the syllabus for the course requires. Solve by substitution Solve using elimination Solve using matrices Solve using determinants