Presentation Index

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Presentation Index
Graphing Equations of Lines
QUIZ Graphing Equations of Lines
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SORRY, incorrect answer!Try Again!
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Chapter 2 Section 3Graphing Linear Equations
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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.

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Methods of Graphing

• Table of Values

• 2) x- and y-intercepts

3) Slope-intercept form (ymxb)
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Table of Values

• Steps
• List 5 numbers (x) in the table.
• Substitute each x into the equation to find y.
• Plot all of the coordinates.
• Connect the dots to make a line.

x y
-4 ?
-2 ?
0 ?
2 ?
4 ?
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Table of Values

• Steps
• List 5 numbers (x) in the table.
• Substitute each x into the equation to find y.
• Plot all of the coordinates.
• Connect the dots to make a line.

• y3x2

x y
-4 ? -10
-2 ? -4
0 ?
2 ?
4 ?
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Table of Values

• Steps
• List 5 numbers (x) in the table.
• Substitute each x into the equation to find y.
• Plot all of the coordinates.
• Connect the dots to make a line.

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Table of Values

• Steps
• List 5 numbers (x) in the table.
• Substitute each x into the equation to find y.
• Plot all of the coordinates.
• Connect the dots to make a line.

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STOP!

• Work on the
• Try These
• 1-2 on the
• Note Sheet
• (You only need to do a table
• with three values)

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Table of Values

• Practice
• y 2x - 5
• Does your graph look like this?

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Table of Values

• Practice
• x 3y 6
• Does your graph look like this?

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X- and Y-InterceptsWhat are they?

• 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)

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X- and Y-Intercepts

• Steps
• 1) Find the x-intercept of the line
• (evaluate when y0)
• 2) Find the y-intercept of the line
• (evaluate when x0)
• 3) Plot the two ordered pairs (,0) and (0,)
• 4) Connect the dots to make a line.

y2x-6

• x-intercept
• y2x-6
• 02x-6
• 6 6
• 62x
• 2
• 3x
• x-intercept (3,0)

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X- and Y-Intercepts

• Steps
• 1) Find the x-intercept of the line
• (evaluate when y0)
• 2) Find the y-intercept of the line
• (evaluate when x0)
• 3) Plot the two ordered pairs (,0) and (0,)
• 4) Connect the dots to make a line.

y2x-6

• y-intercept
• y2x-6
• y2(0)-6
• y0-6
• y -6
• y-intercept (0,-6)

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X- and Y-Intercepts
y2x-6 x-intercept (3,0) y-intercept (0,-6)

• Steps
• 1) Find the x-intercept of the line
• (evaluate when y0)
• 2) Find the y-intercept of the line
• (evaluate when x0)
• 3) Plot the two ordered pairs (,0) and (0,)
• 4) Connect the dots to make a line.

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X- and Y-Intercepts
y2x-6 x-intercept (3,0) y-intercept (0,-6)

• Steps
• 1) Find the x-intercept of the line
• (evaluate when y0)
• 2) Find the y-intercept of the line
• (evaluate when x0)
• 3) Plot the two ordered pairs (,0) and (0,)
• 4) Connect the dots to make a line.

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STOP!

• Work on the
• Try These
• 1 2 on the
• Note Sheet

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X- and Y-Intercepts

• Practice
• y 3x - 5
• Does your graph look like this?

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X- and Y-Intercepts

• Practice
• x 2y 6
• Does your graph look like this?

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Slope-Intercept Form

• ymxb

Slope
y-intercept

• Steps
• Set the equation equal to y (y?).
• Identify the slope and y-intercept.
• Plot the y-intercept.
• Use slope to count to the next point.
• Connect the dots to make a line.

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Slope-Intercept Form

• Steps
• Set the equation equal to y (y?).
• Identify the slope and y-intercept.
• Plot the y-intercept.
• Use slope to count to the next point.
• Connect the dots to make a line.

• -2xy -3

2x
2x
y2x-3
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Slope-Intercept Form

• Steps
• Set the equation equal to y (y?).
• Identify the slope and y-intercept.
• Plot the y-intercept.
• Use slope to count to the next point.
• Connect the dots to make a line.

y2x-3
Slope
y-intercept
Slope 2 y-intercept -3
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Slope-Intercept Form

• Steps
• Set the equation equal to y (y?).
• Identify the slope and y-intercept.
• Plot the y-intercept.
• Use slope to count to the next point.
• Connect the dots to make a line.

Slope 2 y-intercept -3
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Slope-Intercept Form

• Steps
• Set the equation equal to y (y?).
• Identify the slope and y-intercept.
• Plot the y-intercept.
• Use slope to count to the next point.
• Connect the dots to make a line.

Slope 2 y-intercept -3
Rise Run
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Slope-Intercept Form

• Steps
• Set the equation equal to y (y?).
• Identify the slope and y-intercept.
• Plot the y-intercept.
• Use slope to count to the next point.
• Connect the dots to make a line.

Slope 2 y-intercept -3
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STOP!

• Work on the
• Try These
• 1 2 on the
• Note Sheet

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Slope-Intercept Form

• Practice
• Y 2/3x 1
• Does your graph look like this?

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Slope-Intercept Form

• Practice
• 2) 2x y 3
• Does your graph look like this?

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Vertical Lines
X -5

• The x-coordinates of the points on a vertical
  line are the same.
• The slope of any vertical line is undefined.
• Equations of vertical lines are written
• x the value of the x-coordinate.

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Horizontal Lines

• The y-coordinates of the points on a horizontal
  line are the same.
• The slope of any horizontal line is 0.
• Equations of horizontal lines are written
• y the value of the y-coordinate.

Y 3
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Graphing Review

• Table of Values

• 2) X- and Y-Intercepts

3) Slope-Intercept form (ymxb)
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Which of the following is NOT a Table of Values
for y2x-4?
x y
-4 -12
-2 -8
0 -4
1 -2
3 2
x y
-5 -14
-1 -6
0 -4
1 -2
3 2
x y
-5 -14
-3 -11
0 -4
3 2
4 4
x y
-2 -8
-1 -6
0 -4
4 4
5 6
A
B
C
D
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What are the x- and y-intercepts?

• 2x3y6

• (2,0) (0,3)
• (2,3) (3,2)
• (3,2) (0,0)
• (0,2) (3,0)

A
B
C
D
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Identify the slope and y-intercept.

• 8xy -7

• Slope -8, y-intercept 7
• Slope -8, y-intercept -7
• Slope 8, y-intercept -7
• Slope 8, y-intercept 7

A
B
C
D
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Identify the graph of y x-3
A
B
C
D
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Identify the graph of x3y9
D
C
B
A
A
B
C
D
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Great Job!You have completed the quiz.

• You may now begin your homework assignment.