Presentation Index Graphing Equations of Lines QUIZ: Graphing Equations of Lines

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Chapter 2 Section 3 Graphing Linear Equations

What is a Linear Equation? A linear equation in two variables is an equation that can be written in standard form as Ax + By = C where A, B, and C are real numbers and A and B are not both 0.

Methods of Graphing 1)Table of Values 2) x- and y-intercepts 3) Slope-intercept form (y=mx+b)

Table of Values Steps: 1.List 5 numbers (x) in the table. 2.Substitute each x into the equation to find y. 3.Plot all of the coordinates. 4.Connect the dots to make a line. xy -4? -2? 0? 2? 4?

Table of Values y=3x+2 xy -4? ? -4 0? 2? 4? Steps: 1.List 5 numbers (x) in the table. 2.Substitute each x into the equation to find y. 3.Plot all of the coordinates. 4.Connect the dots to make a line. Y=3x+2 Y=3(-4)+2 Y= Y= -10 Y=3x+2 Y=3(-2)+2 Y= -6+2 Y= -4 Use all the numbers!!

Table of Values Steps: 1.List 5 numbers (x) in the table. 2.Substitute each x into the equation to find y. 3.Plot all of the coordinates. 4.Connect the dots to make a line.

Table of Values Steps: 1.List 5 numbers (x) in the table. 2.Substitute each x into the equation to find y. 3.Plot all of the coordinates. 4.Connect the dots to make a line.

STOP! Work on the “ Try These ” #1-2 on the Note Sheet (You only need to do a table with three values)

Table of Values Practice: 1) y = 2x - 5 Does your graph look like this? #1

Table of Values Practice: 2) x + 3y = 6 Does your graph look like this? #2

x-intercept: The point where the line crosses the x-axis. –To find, let y = 0 and find the value of x. –Write as an ordered pair (x, 0) y-intercept: The point where the line crosses the y-axis. –To find, let x = 0 and find the value of y. –Write as an ordered pair (0, y) X- and Y-Intercepts What are they?

X- and Y-Intercepts Steps: 1)Find the x-intercept of the line (evaluate when y=0) 2)Find the y-intercept of the line (evaluate when x=0) 3)Plot the two ordered pairs (#,0) and (0,#) 4)Connect the dots to make a line. x-intercept y=2x-6 0=2x =2x2 3=x x-intercept: (3,0) y=2x-6

X- and Y-Intercepts Steps: 1)Find the x-intercept of the line (evaluate when y=0) 2)Find the y-intercept of the line (evaluate when x=0) 3)Plot the two ordered pairs (#,0) and (0,#) 4)Connect the dots to make a line. y=2x-6 y-intercept y=2x-6 y=2(0)-6 y=0-6 y= -6 y-intercept: (0,-6)

X- and Y-Intercepts Steps: 1)Find the x-intercept of the line (evaluate when y=0) 2)Find the y-intercept of the line (evaluate when x=0) 3)Plot the two ordered pairs (#,0) and (0,#) 4)Connect the dots to make a line. y=2x-6 x-intercept: (3,0) y-intercept: (0,-6)

X- and Y-Intercepts Steps: 1)Find the x-intercept of the line (evaluate when y=0) 2)Find the y-intercept of the line (evaluate when x=0) 3)Plot the two ordered pairs (#,0) and (0,#) 4)Connect the dots to make a line. y=2x-6 x-intercept: (3,0) y-intercept: (0,-6)

STOP! Work on the “ Try These ” #1 – 2 on the Note Sheet

Practice: 1) y = 3x - 5 Does your graph look like this? X- and Y-Intercepts #1

Practice: 2) x + 2y = 6 Does your graph look like this? X- and Y-Intercepts #2

y=mx+b Steps: 1.Set the equation equal to y (y=?). 2.Identify the slope and y-intercept. 3.Plot the y-intercept. 4.Use slope to count to the next point. 5.Connect the dots to make a line. Slope-Intercept Form Slopey-intercept

-2x+y= -3 Slope-Intercept Form Steps: 1.Set the equation equal to y (y=?). 2.Identify the slope and y-intercept. 3.Plot the y-intercept. 4.Use slope to count to the next point. 5.Connect the dots to make a line. +2x y=2x-3

Slope-Intercept Form Steps: 1.Set the equation equal to y (y=?). 2.Identify the slope and y-intercept. 3.Plot the y-intercept. 4.Use slope to count to the next point. 5.Connect the dots to make a line. y=2x-3 Slope y-intercept Slope: 2 y-intercept: -3

Slope-Intercept Form Steps: 1.Set the equation equal to y (y=?). 2.Identify the slope and y-intercept. 3.Plot the y- intercept. 4.Use slope to count to the next point. 5.Connect the dots to make a line. Slope: 2 y-intercept: -3

Slope-Intercept Form Steps: 1.Set the equation equal to y (y=?). 2.Identify the slope and y-intercept. 3.Plot the y-intercept. 4.Use slope to count to the next point. 5.Connect the dots to make a line. Slope: 2 y-intercept: -3 Rise Run

Slope-Intercept Form Steps: 1.Set the equation equal to y (y=?). 2.Identify the slope and y-intercept. 3.Plot the y-intercept. 4.Use slope to count to the next point. 5.Connect the dots to make a line. Slope: 2 y-intercept: -3

STOP! Work on the “ Try These ” #1 – 2 on the Note Sheet

Practice: 1)Y = 2 / 3 x + 1 Does your graph look like this? Slope-Intercept Form #1

Practice: 2) 2x + y = 3 Does your graph look like this? Slope-Intercept Form #2

Vertical Lines 1)The x-coordinates of the points on a vertical line are the same. 2)The slope of any vertical line is undefined. 3)Equations of vertical lines are written x = the value of the x- coordinate. X = -5

1)The y-coordinates of the points on a horizontal line are the same. 2)The slope of any horizontal line is 0. 3)Equations of horizontal lines are written y = the value of the y- coordinate. Horizontal Lines Y = 3

Graphing Review 1)Table of Values 2) X- and Y-Intercepts 3) Slope-Intercept form (y=mx+b)

Which of the following is NOT a Table of Values for y=2x-4? xy xy xy xy ABCD

What are the x- and y-intercepts? A B C D 2x+3y=6  (2,0) & (0,3)  (2,3) & (3,2)  (3,2) & (0,0)  (0,2) & (3,0)

Identify the slope and y-intercept. A B C D  Slope: -8, y-intercept: 7  Slope: -8, y-intercept: -7  Slope: 8, y-intercept: -7  Slope: 8, y-intercept: 7 8x+y= -7

Identify the graph of y= x-3 A B C D

Identify the graph of x+3y=9 ABCD A B C D

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