Week 1 discussion : Systems of linear equations
0 likes1,075 views
Read the explanation in each lesson carefully, then study the examples given before doing the exercises.
1 of 4
Downloaded 17 times
Recommended
Slope power point grade 8
Slope power point grade 8ginacdl
油
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.Module Four Lesson 2 Remediation Notes - Slope intercept form
Module Four Lesson 2 Remediation Notes - Slope intercept formncvpsmanage1
油
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.Slopeinterceptform
SlopeinterceptformKristineCarr1
油
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.Slope and y intercept
Slope and y interceptbillingssr
油
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.Writing linear equations KG Math Middle School
Writing linear equations KG Math Middle SchoolKellie Greenrod
油
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.Review Of Slope And The Slope Intercept Formula
Review Of Slope And The Slope Intercept Formulataco40
油
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.Linear Functions
Linear Functionskliegey524
油
Linear functions have a constant rate of change (slope) between any two points. The document provides methods for determining if a set of data represents a linear function, writing the equation of a line given various parameters like slope and intercepts, and properties of lines like parallel, perpendicular, vertical and horizontal lines. It also discusses how to find the equation of a perpendicular bisector by calculating the slope, midpoint and using the negative reciprocal slope in the point-slope form.4 6 equations of lines
4 6 equations of linesgwilson8786
油
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.Introduction to slope presentation
Introduction to slope presentationskellyreyes
油
This document defines slope and provides examples for teaching students about slope. It explains that slope is the ratio of vertical to horizontal change and can be positive, negative, zero, or undefined. The objectives are for students to identify slope from graphs, calculate slope using rise over run, and apply the slope formula to find slope given two points. Examples are provided to demonstrate calculating slope from graphs and points using rise over run and the slope formula.Writing and Graphing slope intercept form
Writing and Graphing slope intercept formguestd1dc2e
油
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.Stair on slope of a line
Stair on slope of a linekelleycunningham
油
This document discusses the concept of slope and how to calculate it. It defines slope as measuring the steepness of a line and explains that it is calculated by finding the rise over the run between two points on a line. The document then provides examples of slopes for lines that are positive, negative, zero, and undefined (vertical) and shows the corresponding graphs in slope-intercept form. It concludes with practice problems calculating slope from graphs, equations, and point pairs.Graph of linear function
Graph of linear functionMartinGeraldine
油
Graph are often used to visualize the relationship between two variables. The graph of a linear function is always a straight line. There are two common approaches to graphing a linear function from its equation: 1) using the slope-intercept form which identifies the slope and y-intercept directly from the equation, and 2) using the x- and y-intercepts which involves substituting values of 0 for x and y to find the two points needed to draw the line. Both approaches are illustrated through examples of graphing different linear equations.Identifying slope and y intercept
Identifying slope and y interceptrobertleichner
油
The document discusses the equation of a line, y=mx+b, and its key components of slope and y-intercept. It defines slope as the rate of rise or fall of a line and provides the formula to calculate it between two points. It also defines the y-intercept as the point where the line crosses the y-axis. The document provides examples of lines with their slopes and y-intercepts calculated from points and used to write the equation of the line.Finding slope
Finding slopemccallr
油
This is a ppt for learning how to calculate the slope of a line within a line graph. This ppt works for about a 8th t 9th grade level.Linear equation
Linear equationRobinFilter
油
1) The document discusses linear equations in slope-intercept (y=mx+b) and standard (ax+by=c) form. It provides examples of writing equations from graphs and vice versa.
2) Transformations of linear and quadratic equations are introduced, where changing coefficients or adding constants changes the graph by shifting it up/down or left/right.
3) Examples of graphing quadratic equations y=x^2 and transformations y=x^2+c and y=kx^2+c are shown and described.Standard form solve equations
Standard form solve equationspfefferteacher
油
The document discusses standard form for linear equations and provides examples of converting equations to standard form. It also discusses writing equations of lines given different forms, including slope-intercept form, standard form, and point-slope form. Steps are provided for solving two-step equations by using the opposite operations to isolate the variable. Examples demonstrate converting equations to standard form, writing equations given the slope and y-intercept or two points, and solving a two-step equation.4 5 slope
4 5 slopegwilson8786
油
The document discusses slope and how it can be used to help a pilot adjust their flight path to clear an obstacle like a mountain. It defines slope as the ratio of the rise (vertical change) over the run (horizontal change) between two points on a line. By communicating the required slope to the pilot, the person could tell them how much they need to change their altitude relative to the distance they need to travel horizontally in order to safely pass over the mountain without crashing into it.5.5 Point Slope and Standard Form
5.5 Point Slope and Standard Formramjdram
油
This document provides instructions for students to complete algebra warm up problems involving graphing lines from equations. It outlines three methods for graphing lines: using the slope and y-intercept, using a T-chart, and manipulating equations into slope-intercept form. Students are informed they will be tested on using both the slope-intercept method and the T-chart method for graphing lines from equations. They are also told they will need to learn how to manipulate equations in standard form and point-slope form into slope-intercept form.Linear functions
Linear functionshalcr1ja
油
The document discusses different forms and methods for graphing linear functions, including:
1) The standard, point-slope, and slope-intercept forms of linear equations.
2) Converting between these forms by solving for slope and y-intercept.
3) Graphing linear functions by finding the slope from two points using the point-slope form, making a table of x-y values, or finding the x- and y-intercepts.
4) Determining if two functions are parallel or perpendicular based on having equal or reciprocal slopes.Graphing lines using slopeintercept
Graphing lines using slopeinterceptluna dionson
油
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.January 9, 2014
January 9, 2014khyps13
油
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.Linear equations
Linear equationscathyguyer
油
This document discusses linear equations in the form y=mx+b. It defines slope as rise over run, and the y-intercept as the point where the line crosses the y-axis. It provides examples of special lines with undefined or zero slopes. It explains how to find the equation of a line given two points, given slope and a point, or given just the slope and y-intercept. It also notes how to graph lines by starting at the y-intercept and moving up the rise and over the run.Finding The Slope And Y Intercept
Finding The Slope And Y InterceptThief River Falls
油
The document discusses how to identify the slope and y-intercept of a line given in standard form. It shows working through examples of changing lines from standard form (Ax + By = C) to slope-intercept form (y = mx + b). Through solving the equations for y, the slope (m) and y-intercept (b) can be determined. Graphing lines on a coordinate plane is also demonstrated.Slope intercept
Slope interceptHuron School District
油
The document discusses converting linear equations to slope-intercept form (y=mx+b). It provides examples of converting equations like 2x+1, 5y=10x+15, and -3y=-9x-12 to slope-intercept form and finding the slope and y-intercept. It also defines x-intercept and y-intercept and shows how to find them by letting x=0 or y=0 and solving the equation.1.4.3 Slopes and Equations of Lines
1.4.3 Slopes and Equations of Linessmiller5
油
The document discusses slopes and equations of lines. It defines slope as rise over run and explains how to calculate slope from two points on a line or from the graph of a line. It also explains how to write the equation of a line in point-slope form, slope-intercept form, or for horizontal and vertical lines. Several examples are provided of finding slopes and writing line equations in different forms.8.3 Slope And Y Intercept
8.3 Slope And Y InterceptJessca Lundin
油
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.5.5 parallel perp lines
5.5 parallel perp linescageke
油
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.1.3.2C Equations of Lines
1.3.2C Equations of Linessmiller5
油
* Find the slope of a line.
* Use slopes to identify parallel and perpendicular lines.
* Write the equation of a line through a given point
- parallel to a given line
- perpendicular to a given line
WRITING AND GRAPHING LINEAR EQUATIONS 1.pptx
WRITING AND GRAPHING LINEAR EQUATIONS 1.pptxKristenHathcock
油
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.identities1.2
identities1.2John Michael Liguan
油
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.More Related Content
What's hot (20)
Introduction to slope presentation
Introduction to slope presentationskellyreyes
油
This document defines slope and provides examples for teaching students about slope. It explains that slope is the ratio of vertical to horizontal change and can be positive, negative, zero, or undefined. The objectives are for students to identify slope from graphs, calculate slope using rise over run, and apply the slope formula to find slope given two points. Examples are provided to demonstrate calculating slope from graphs and points using rise over run and the slope formula.Writing and Graphing slope intercept form
Writing and Graphing slope intercept formguestd1dc2e
油
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.Stair on slope of a line
Stair on slope of a linekelleycunningham
油
This document discusses the concept of slope and how to calculate it. It defines slope as measuring the steepness of a line and explains that it is calculated by finding the rise over the run between two points on a line. The document then provides examples of slopes for lines that are positive, negative, zero, and undefined (vertical) and shows the corresponding graphs in slope-intercept form. It concludes with practice problems calculating slope from graphs, equations, and point pairs.Graph of linear function
Graph of linear functionMartinGeraldine
油
Graph are often used to visualize the relationship between two variables. The graph of a linear function is always a straight line. There are two common approaches to graphing a linear function from its equation: 1) using the slope-intercept form which identifies the slope and y-intercept directly from the equation, and 2) using the x- and y-intercepts which involves substituting values of 0 for x and y to find the two points needed to draw the line. Both approaches are illustrated through examples of graphing different linear equations.Identifying slope and y intercept
Identifying slope and y interceptrobertleichner
油
The document discusses the equation of a line, y=mx+b, and its key components of slope and y-intercept. It defines slope as the rate of rise or fall of a line and provides the formula to calculate it between two points. It also defines the y-intercept as the point where the line crosses the y-axis. The document provides examples of lines with their slopes and y-intercepts calculated from points and used to write the equation of the line.Finding slope
Finding slopemccallr
油
This is a ppt for learning how to calculate the slope of a line within a line graph. This ppt works for about a 8th t 9th grade level.Linear equation
Linear equationRobinFilter
油
1) The document discusses linear equations in slope-intercept (y=mx+b) and standard (ax+by=c) form. It provides examples of writing equations from graphs and vice versa.
2) Transformations of linear and quadratic equations are introduced, where changing coefficients or adding constants changes the graph by shifting it up/down or left/right.
3) Examples of graphing quadratic equations y=x^2 and transformations y=x^2+c and y=kx^2+c are shown and described.Standard form solve equations
Standard form solve equationspfefferteacher
油
The document discusses standard form for linear equations and provides examples of converting equations to standard form. It also discusses writing equations of lines given different forms, including slope-intercept form, standard form, and point-slope form. Steps are provided for solving two-step equations by using the opposite operations to isolate the variable. Examples demonstrate converting equations to standard form, writing equations given the slope and y-intercept or two points, and solving a two-step equation.4 5 slope
4 5 slopegwilson8786
油
The document discusses slope and how it can be used to help a pilot adjust their flight path to clear an obstacle like a mountain. It defines slope as the ratio of the rise (vertical change) over the run (horizontal change) between two points on a line. By communicating the required slope to the pilot, the person could tell them how much they need to change their altitude relative to the distance they need to travel horizontally in order to safely pass over the mountain without crashing into it.5.5 Point Slope and Standard Form
5.5 Point Slope and Standard Formramjdram
油
This document provides instructions for students to complete algebra warm up problems involving graphing lines from equations. It outlines three methods for graphing lines: using the slope and y-intercept, using a T-chart, and manipulating equations into slope-intercept form. Students are informed they will be tested on using both the slope-intercept method and the T-chart method for graphing lines from equations. They are also told they will need to learn how to manipulate equations in standard form and point-slope form into slope-intercept form.Linear functions
Linear functionshalcr1ja
油
The document discusses different forms and methods for graphing linear functions, including:
1) The standard, point-slope, and slope-intercept forms of linear equations.
2) Converting between these forms by solving for slope and y-intercept.
3) Graphing linear functions by finding the slope from two points using the point-slope form, making a table of x-y values, or finding the x- and y-intercepts.
4) Determining if two functions are parallel or perpendicular based on having equal or reciprocal slopes.Graphing lines using slopeintercept
Graphing lines using slopeinterceptluna dionson
油
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.January 9, 2014
January 9, 2014khyps13
油
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.Linear equations
Linear equationscathyguyer
油
This document discusses linear equations in the form y=mx+b. It defines slope as rise over run, and the y-intercept as the point where the line crosses the y-axis. It provides examples of special lines with undefined or zero slopes. It explains how to find the equation of a line given two points, given slope and a point, or given just the slope and y-intercept. It also notes how to graph lines by starting at the y-intercept and moving up the rise and over the run.Finding The Slope And Y Intercept
Finding The Slope And Y InterceptThief River Falls
油
The document discusses how to identify the slope and y-intercept of a line given in standard form. It shows working through examples of changing lines from standard form (Ax + By = C) to slope-intercept form (y = mx + b). Through solving the equations for y, the slope (m) and y-intercept (b) can be determined. Graphing lines on a coordinate plane is also demonstrated.Slope intercept
Slope interceptHuron School District
油
The document discusses converting linear equations to slope-intercept form (y=mx+b). It provides examples of converting equations like 2x+1, 5y=10x+15, and -3y=-9x-12 to slope-intercept form and finding the slope and y-intercept. It also defines x-intercept and y-intercept and shows how to find them by letting x=0 or y=0 and solving the equation.1.4.3 Slopes and Equations of Lines
1.4.3 Slopes and Equations of Linessmiller5
油
The document discusses slopes and equations of lines. It defines slope as rise over run and explains how to calculate slope from two points on a line or from the graph of a line. It also explains how to write the equation of a line in point-slope form, slope-intercept form, or for horizontal and vertical lines. Several examples are provided of finding slopes and writing line equations in different forms.8.3 Slope And Y Intercept
8.3 Slope And Y InterceptJessca Lundin
油
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.5.5 parallel perp lines
5.5 parallel perp linescageke
油
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.1.3.2C Equations of Lines
1.3.2C Equations of Linessmiller5
油
* Find the slope of a line.
* Use slopes to identify parallel and perpendicular lines.
* Write the equation of a line through a given point
- parallel to a given line
- perpendicular to a given line
Similar to Week 1 discussion : Systems of linear equations (20)
WRITING AND GRAPHING LINEAR EQUATIONS 1.pptx
WRITING AND GRAPHING LINEAR EQUATIONS 1.pptxKristenHathcock
油
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.identities1.2
identities1.2John Michael Liguan
油
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.Slope intercept
Slope interceptcoolhanddav
油
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 equations 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 from word problems and finding values of the functions. A quiz reviews writing equations from slopes and points and graphing lines from their equations.Chapter 5 Slope-Intercept Form
Chapter 5 Slope-Intercept FormIinternational Program School
油
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.
slope_and_linear_eq--section_1.4.ppt
slope_and_linear_eq--section_1.4.pptLailaBalinadoLunduya
油
Slope describes the steepness of a line, with positive slope indicating a line rising from left to right and negative slope indicating a line falling from left to right. Slope is calculated as the rise over the run between two points and is commonly represented by m. There are several ways to find the equation of a line given certain information: if given the slope and y-intercept, the equation is y = mx + b; if given two points, slope is calculated as rise over run and then substituted into the point-slope form; if given the slope and one point, the point-slope form can be used. Horizontal lines have a slope of zero while vertical lines have undefined slopes.Linear functions
Linear functionsrugunia
油
A linear function is an equation of the form y = mx + b, where m is the slope and b is the y-intercept. The slope is defined as the ratio of the rise over the run between any two points on the line. Lines with the same slope are parallel, while lines with slopes that are negative reciprocals of each other are perpendicular. There are also horizontal and vertical lines, where horizontal lines have a slope of 0 and vertical lines have an undefined slope. The point-slope form of a line is used to find the equation of a line given a point and the slope.Linear Equations in Two Variables.pptx
Linear Equations in Two Variables.pptxCamiling Catholic School
油
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.12 LINEAR EQUATIONS.ppt
12 LINEAR EQUATIONS.pptElmabethDelaCruz1
油
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.topic number 1 -slope of the line final.pptx
topic number 1 -slope of the line final.pptxlandoyjennilyn
油
slope of the line. determine the slope of the line. discuss slope. solveLESSON PROPER_04-Graphing linear equations in two variables.pptx
LESSON PROPER_04-Graphing linear equations in two variables.pptxroxane47
油
LESSON PROPER_04-Graphing linear equations in two variables.pptxLESSON PROPER_04-Graphing linear equations in two variables.pptx
LESSON PROPER_04-Graphing linear equations in two variables.pptxroxane47
油
LESSON PROPER_04-Graphing linear equations in two variables.pptxModule 1 plane coordinate geometry
Module 1 plane coordinate geometrydionesioable
油
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.1554 linear equations in two variables
1554 linear equations in two variablesDr Fereidoun Dejahang
油
Mathematics (from Greek 亮略慮侶亮留 m叩thma, 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 mathematicschapter1_part2.pdf
chapter1_part2.pdfAliEb2
油
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.Slop lecture
Slop lectureAdnanBukhari13
油
Slope describes the steepness of a line and is defined as the rise over the run between two points on a line. It can be positive, negative, zero, or undefined. To determine the slope of a line, two points are identified and the change in y-values (rise) is divided by the change in x-values (run). The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. To graph a line using slope-intercept form, the y-intercept is plotted and then additional points are determined by applying the slope using rise-over-run from the previous point.Linear equations rev
Linear equations revAKASHKENE
油
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.February 18 2016
February 18 2016khyps13
油
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 between2.2 slope
2.2 slopefthrower
油
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.Slope Powerpoint
Slope Powerpointguesta9ee9b
油
This document discusses graphing linear equations using the slope-intercept form. It explains that the slope-intercept form gives the y-intercept and slope, allowing you to graph the line without making a table of points. You plot the y-intercept on the y-axis, then use the slope to plot additional points and draw the line. Examples are given of graphing different equations in slope-intercept form by finding the y-intercept and slope from the given equation.Recently uploaded (20)
Gojek Clone Multi-Service Super App.pptx
Gojek Clone Multi-Service Super App.pptxV3cube
油
Gojek Clone is a versatile multi-service super app that offers ride-hailing, food delivery, payment services, and more, providing a seamless experience for users and businesses alike on a single platform.How Discord Indexes Trillions of Messages: Scaling Search Infrastructure by V...
How Discord Indexes Trillions of Messages: Scaling Search Infrastructure by V...ScyllaDB
油
This talk shares how Discord scaled their message search infrastructure using Rust, Kubernetes, and a multi-cluster Elasticsearch architecture to achieve better performance, operability, and reliability, while also enabling new search features for Discord users.Technology use over time and its impact on consumers and businesses.pptx
Technology use over time and its impact on consumers and businesses.pptxkaylagaze
油
In this presentation, I explore how technology has changed consumer behaviour and its impact on consumers and businesses. I will focus on internet access, digital devices, how customers search for information and what they buy online, video consumption, and lastly consumer trends.BoxLang JVM Language : The Future is Dynamic
BoxLang JVM Language : The Future is DynamicOrtus Solutions, Corp
油
Just like life, our code must evolve to meet the demands of an ever-changing world. Adaptability is key in developing for the web, tablets, APIs, or serverless applications. Multi-runtime development is the future, and that future is dynamic. Enter BoxLang: Dynamic. Modular. Productive. (www.boxlang.io)
BoxLang transforms development with its dynamic design, enabling developers to write expressive, functional code effortlessly. Its modular architecture ensures flexibility, allowing easy integration into your existing ecosystems.
Interoperability at Its Core
BoxLang boasts 100% interoperability with Java, seamlessly blending traditional and modern development practices. This opens up new possibilities for innovation and collaboration.
Multi-Runtime Versatility
From a compact 6MB OS binary to running on our pure Java web server, CommandBox, Jakarta EE, AWS Lambda, Microsoft Functions, WebAssembly, Android, and more, BoxLang is designed to adapt to any runtime environment. BoxLang combines modern features from CFML, Node, Ruby, Kotlin, Java, and Clojure with the familiarity of Java bytecode compilation. This makes it the go-to language for developers looking to the future while building a solid foundation.
Empowering Creativity with IDE Tools
Unlock your creative potential with powerful IDE tools designed for BoxLang, offering an intuitive development experience that streamlines your workflow. Join us as we redefine JVM development and step into the era of BoxLang. Welcome to the future.
Technology use over time and its impact on consumers and businesses.pptx
Technology use over time and its impact on consumers and businesses.pptxkaylagaze
油
In this presentation, I will discuss how technology has changed consumer behaviour and its impact on consumers and businesses. I will focus on internet access, digital devices, how customers search for information and what they buy online, video consumption, and lastly consumer trends.
Inside Freshworks' Migration from Cassandra to ScyllaDB by Premkumar Patturaj
Inside Freshworks' Migration from Cassandra to ScyllaDB by Premkumar PatturajScyllaDB
油
Freshworks migrated from Cassandra to ScyllaDB to handle growing audit log data efficiently. Cassandra required frequent scaling, complex repairs, and had non-linear scaling. ScyllaDB reduced costs with fewer machines and improved operations. Using Zero Downtime Migration (ZDM), they bulk-migrated data, performed dual writes, and validated consistency.THE BIG TEN BIOPHARMACEUTICAL MNCs: GLOBAL CAPABILITY CENTERS IN INDIA
THE BIG TEN BIOPHARMACEUTICAL MNCs: GLOBAL CAPABILITY CENTERS IN INDIASrivaanchi Nathan
油
This business intelligence report, "The Big Ten Biopharmaceutical MNCs: Global Capability Centers in India", provides an in-depth analysis of the operations and contributions of the Global Capability Centers (GCCs) of ten leading biopharmaceutical multinational corporations in India. The report covers AstraZeneca, Bayer, Bristol Myers Squibb, GlaxoSmithKline (GSK), Novartis, Sanofi, Roche, Pfizer, Novo Nordisk, and Eli Lilly. In this report each company's GCC is profiled with details on location, workforce size, investment, and the strategic roles these centers play in global business operations, research and development, and information technology and digital innovation.SMART SENTRY CYBER THREAT INTELLIGENCE IN IIOT
SMART SENTRY CYBER THREAT INTELLIGENCE IN IIOTTanmaiArni
油
SMART SENTRY CYBER THREAT INTELLIGENCE IN IIOTBackstage Software Templates for Java Developers
Backstage Software Templates for Java DevelopersMarkus Eisele
油
As a Java developer you might have a hard time accepting the limitations that you feel being introduced into your development cycles. Let's look at the positives and learn everything important to know to turn Backstag's software templates into a helpful tool you can use to elevate the platform experience for all developers.Endpoint Backup: 3 Reasons MSPs Ignore It
Endpoint Backup: 3 Reasons MSPs Ignore ItMSP360
油
Many MSPs overlook endpoint backup, missing out on additional profit and leaving a gap that puts client data at risk.
Join our webinar as we break down the top challenges of endpoint backupand how to overcome them.Replacing RocksDB with ScyllaDB in Kafka Streams by Almog Gavra
Replacing RocksDB with ScyllaDB in Kafka Streams by Almog GavraScyllaDB
油
Learn how Responsive replaced embedded RocksDB with ScyllaDB in Kafka Streams, simplifying the architecture and unlocking massive availability and scale. The talk covers unbundling stream processors, key ScyllaDB features tested, and lessons learned from the transition.TrustArc Webinar - Building your DPIA/PIA Program: Best Practices & Tips
TrustArc Webinar - Building your DPIA/PIA Program: Best Practices & TipsTrustArc
油
Understanding DPIA/PIAs and how to implement them can be the key to embedding privacy in the heart of your organization as well as achieving compliance with multiple data protection / privacy laws, such as GDPR and CCPA. Indeed, the GDPR mandates Privacy by Design and requires documented Data Protection Impact Assessments (DPIAs) for high risk processing and the EU AI Act requires an assessment of fundamental rights.
How can you build this into a sustainable program across your business? What are the similarities and differences between PIAs and DPIAs? What are the best practices for integrating PIAs/DPIAs into your data privacy processes?
Whether you're refining your compliance framework or looking to enhance your PIA/DPIA execution, this session will provide actionable insights and strategies to ensure your organization meets the highest standards of data protection.
Join our panel of privacy experts as we explore:
- DPIA & PIA best practices
- Key regulatory requirements for conducting PIAs and DPIAs
- How to identify and mitigate data privacy risks through comprehensive assessments
- Strategies for ensuring documentation and compliance are robust and defensible
- Real-world case studies that highlight common pitfalls and practical solutions[Webinar] Scaling Made Simple: Getting Started with No-Code Web Apps![[Webinar] Scaling Made Simple: Getting Started with No-Code Web Apps](https://cdn.slidesharecdn.com/ss_thumbnails/webinarscalingmadesimplegettingstartedwithno-codewebapps-mar52025-250305183437-f03c78a3-thumbnail.jpg?width=560&fit=bounds)
[Webinar] Scaling Made Simple: Getting Started with No-Code Web AppsSafe Software
油
Ready to simplify workflow sharing across your organization without diving into complex coding? With FME Flow Apps, you can build no-code web apps that make your data work harder for you fast.
In this webinar, well show you how to:
Build and deploy Workspace Apps to create an intuitive user interface for self-serve data processing and validation.
Automate processes using Automation Apps. Learn to create a no-code web app to kick off workflows tailored to your needs, trigger multiple workspaces and external actions, and use conditional filtering within automations to control your workflows.
Create a centralized portal with Gallery Apps to share a collection of no-code web apps across your organization.
Through real-world examples and practical demos, youll learn how to transform your workflows into intuitive, self-serve solutions that empower your team and save you time. We cant wait to show you whats possible!Wondershare Filmora Crack 14.3.2.11147 Latest
Wondershare Filmora Crack 14.3.2.11147 Latestudkg888
油
https://ncracked.com/7961-2/
Note: >> Please copy the link and paste it into Google New Tab now Download link
Free Download Wondershare Filmora 14.3.2.11147 Full Version - All-in-one home video editor to make a great video.Free Download Wondershare Filmora for Windows PC is an all-in-one home video editor with powerful functionality and a fully stacked feature set. Filmora has a simple drag-and-drop top interface, allowing you to be artistic with the story you want to create.Video Editing Simplified - Ignite Your Story. A powerful and intuitive video editing experience. Filmora 10 hash two new ways to edit: Action Cam Tool (Correct lens distortion, Clean up your audio, New speed controls) and Instant Cutter (Trim or merge clips quickly, Instant export).Filmora allows you to create projects in 4:3 or 16:9, so you can crop the videos or resize them to fit the size you want. This way, quickly converting a widescreen material to SD format is possible.
UiPath Document Understanding - Generative AI and Active learning capabilities
UiPath Document Understanding - Generative AI and Active learning capabilitiesDianaGray10
油
This session focus on Generative AI features and Active learning modern experience with Document understanding.
Topics Covered:
Overview of Document Understanding
How Generative Annotation works?
What is Generative Classification?
How to use Generative Extraction activities?
What is Generative Validation?
How Active learning modern experience accelerate model training?
Q/A
If you have any questions or feedback, please refer to the "Women in Automation 2025" dedicated Forum thread. You can find there extra details and updates. EaseUS Partition Master Crack 2025 + Serial Key
EaseUS Partition Master Crack 2025 + Serial Keykherorpacca127
油
https://ncracked.com/7961-2/
Note: >> Please copy the link and paste it into Google New Tab now Download link
EASEUS Partition Master Crack is a professional hard disk partition management tool and system partition optimization software. It is an all-in-one PC and server disk management toolkit for IT professionals, system administrators, technicians, and consultants to provide technical services to customers with unlimited use.
EASEUS Partition Master 18.0 Technician Edition Crack interface is clean and tidy, so all options are at your fingertips. Whether you want to resize, move, copy, merge, browse, check, convert partitions, or change their labels, you can do everything with a few clicks. The defragmentation tool is also designed to merge fragmented files and folders and store them in contiguous locations on the hard drive.
Fl studio crack version 12.9 Free Download
Fl studio crack version 12.9 Free Downloadkherorpacca127
油
Google the copied link 嶧 https://activationskey.com/download-latest-setup/
嶧
The ultimate guide to FL Studio 12.9 Crack, the revolutionary digital audio workstation that empowers musicians and producers of all levels. This software has become a cornerstone in the music industry, offering unparalleled creative capabilities, cutting-edge features, and an intuitive workflow.
With FL Studio 12.9 Crack, you gain access to a vast arsenal of instruments, effects, and plugins, seamlessly integrated into a user-friendly interface. Its signature Piano Roll Editor provides an exceptional level of musical expression, while the advanced automation features empower you to create complex and dynamic compositions.Cloud of everything Tech of the 21 century in Aviation
Cloud of everything Tech of the 21 century in AviationAssem mousa
油
AI, Block chain, Digital Currency, Cloud, Cloud of Things, Tactile Internet, Digital Twins, IOT, AR, VR, MR, U commerce, data and robotics."
Week 1 discussion : Systems of linear equations
- 1. Lesson 1.1 Review on Graphing Linear Equations Linear Equations can be graphed using table of values. Example 1. Graph x + y = 10 x 3 5 10 y 7 5 y 0 x + y =10 Plot the three points on the coordinate system and connect . x The graph of the linear equation is presented at the right. y Example 2 Graph x - y = 2 x 0 5 2 y -2 3 0 x-y=2 x
- 2. Another way to graph linear equations in two variables is by using the slope-intercept method. Recall that slope is the steepness or inclination of a line. It is the ratio of the vertical change to the horizontal change, the rise over the run. In the form y = mx + b, m is the slope and b is the y-intercept. So, it is important that we transform the given equation into the y form in order to identify the slope and y-intercept. Remember, two points determine a line. Examples: Transform the equations to y - form. Identify the slope and the y- intercept 1. x + y = 24 y = -x + 24 m = -1, b = 24 2. -4x -y = 5 y = -4x - 5 m = -4, b = -5 3. -x + 2y = 8 y= 1x+4 2 m= 1, b=4 2
- 3. Linear equations can be graphed using the slope-intercept form. Let's graph the equation 3x -2y = 4. Follow the steps. Transform 3x -2y = 4 to y = mx + b y = 3 x - 2. 2 The slope (m) of the equation is 3 and the y- intercept (b) is -2. 2 Locate the y-intercept, -2 at the y-axis. Mark the point associated with this. Starting from the y-intercept move 3 units upward ( rise ) and from this position move 2 units to the right ( run) . Mark this point. ( If the slope is negative move upward then to the left or move downward then to the right) Move again from this point using the ratio of the slope. Mark this point. Connect the points with a straight line. Use three points y Run = 2 x Rise=3 y-intercept This is now the graph of 3x - 2y = 4
- 4. Suppose our equation is -3x -2y = 4 Following the steps the graph now of -3x -2y = 4 is presented at the right. What have you noticed on the slope? Did you find any difference between the two equations and their graphs?