Chapter 7 section 5
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Chapter 7 Section 5. Graphing Linear Equations. What You’ll Learn. You’ll learn to graph linear equations by using the x- and y- intercepts or the slope and y intercept. Why It’s Important. Rates Linear graphs are helpful in showing phone costs. Example 1.

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Chapter 7 Section 5

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Chapter 7 section 5

Chapter 7 Section 5

Graphing Linear Equations


What you ll learn

What You’ll Learn

You’ll learn to graph linear equations by using the x- and y- intercepts or the slope and y intercept.


Why it s important

Why It’s Important

Rates

Linear graphs are helpful in showing phone costs.


Example 1

Example 1

Determine the x-intercept and y-intercept of the graph of each equation. Then graph the equation.

5y – x = 10

To find the x-intercept, let y = 0.

5(0) – x = 10

- x = 10

-1 -1

x = -10

(-10,0)

To find the y-intercept, let x = 0

5y – 0 = 10

5y = 10

5 5

y = 2

(0,2)


Example 1 continued

Example 1: Continued

  • The x-intercept is -10, and the y-intercept is 2. This means that the graph intersects the x- axis at (-10, 0) and the y-axis at (0, 2).

  • Graph these ordered pairs.

  • Then draw the line that passes through these points.


Example 1 continued1

(0, 2)

Example 1: Continued

Y

8

7

6

5

4

3

2

1

0

  • Graph: 5y – x = 10

(-10, 0)

x

-15 -14 -13-12 -11 -10 9 -8 -7 -6 -5 -4 -3 -2 -1


Example 2

Example 2

Determine the x-intercept and y-intercept of the graph of each equation. Then graph the equation.

2x – 4y = 8

To find the x-intercept, let y = 0.

2x – 4(0) = 8

2x = 8

2 2

x = 4

(4, 0)

To find the y-intercept, let x = 0

2(0) – 4y = 8

-4y = 8

-4 -4

y = -2

(0,-2)


Example 2 continued

Example 2: Continued

  • The x-intercept is 4, and the y-intercept is -2. This means that the graph intersects the x- axis at (4, 0) and the y-axis at (0, -2).

  • Graph these ordered pairs.

  • Then draw the line that passes through these points.


Example 2 continued1

(4, 0)

Example 2: Continued

2

1

0

-1

-2

-3

-4

-5

  • Graph: 2x – 4y = 8

x

1 2 3 4 5 6 7 8

(0, -2)

Y


How to check your work

How to Check Your Work

  • Look at the graph.

  • Choose some other point on the line and determine whether it is a solution of 2x – 4y = 8.

  • Try (2, -1)

2x – 4y = 8

2(2) – 4(-1) = 8

4 + 4 = 8

8 = 8


Your turn

Your Turn

Determine the x-intercept and y-intercept of the graph of each equation. Then graph the equation.

x + y = 2


Chapter 7 section 5

x + y = 2

(0, 2)

(2, 0)


Your turn1

Your Turn

Determine the x-intercept and y-intercept of the graph of each equation. Then graph the equation.

3x + y = 3


3x y 3

3x + y = 3

(0, 3)

(1, 0)


Your turn2

Your Turn

Determine the x-intercept and y-intercept of the graph of each equation. Then graph the equation.

4x – 5y = 20


4x 5y 20

4x – 5y = 20

(5, 0)

(0, -4)


Example 3

Example 3

To mail letter in 2000, it cost $0.33 for the first ounce and $0.22 for each additional ounce. This can be represented by y = 0.33 + 0.22x. Determine the slope and y-intercept of the graph of the equation.

y = mx + b

y = 0.22x + 0.33

The slope is 0.22, and the y-intercept is 0.33. So the slope represents the cost per ounce after the first ounce, and the y-intercept represents the cost of the first ounce of mail.


Example 4

Example 4

Determine the slope and y-intercept of the graph of 10 + 5y = 2x.

Write the equation in slope-intercept form to find the slope and y-intercept

10 + 5y = 2x

10 + 5y = 2x

-10 = -10

5y = 2x – 10

5 5

y = ⅖x – 2

The slope is ⅖, and the y-intercept is -2.


Your turn3

Your Turn

Determine the slope and y-intercept.

y = 5x + 9

m = 5, b = 9


Your turn4

Your Turn

Determine the slope and y-intercept.

4x + 3y = 6

m = - 4/3 , b = 2


Example 5

Example 5

Graph each equation by using the slope and y-intercept

y = ⅔x – 5

y = mx + b

y = ⅔x + (-5)

The slope is ⅔, and the y-intercept is -5.

Graph the point at (0, -5).

Then go up 2 units and right 3 units.

This will be the point at (3, -3).

Then draw the line through points at (0, -5) and (3, -3).


Example 5 continued

Example 5: Continued

3

(3, -3)

2

(0, -5)


Example 5 check

Example 5: Check

  • The graph appears to go through the point at (6, -1) . Substitute (6, -1) into y = ⅔x + (-5).

    y = ⅔x + (-5)

    -1 = ⅔(6) + (-5)

    -1 = 4 – 5

    -1 = -1

Replace x with 6 and y with -1.


Example 6

Example 6

Graph each equation by using the slope and y-intercept.

3x + 2y = 6

First, write the equation in slope intercept form.

3x + 2y = 6

-3x = -3x

2y = -3x + 6

2 2

y = -3⁄₂x + 3

The slope is -3⁄₂ and the y-intercept is 3.


Example 6 continued

Example 6: Continued

  • Graph the point (0, 3).

  • Then go up 3 units and left 2 units.

  • This will be the point at (-2, 6).

  • Then draw a line through (0, 3) and (-2, 6).

  • You can check your answer by substituting the coordinates of another point that appears to lie on the line, such as (2, 0).


Example 6 graph

Example 6: Graph

-2

(-2, 6)

3

(0, 3)


Your turn5

Your Turn

Graph each equation by using the slope and y-intercept.

y= ½x + 3


Answer

Answer

(2, 4)

(0, 3)

y = ½x + 3


Your turn6

Your Turn

Graph each equation by using the slope and y-intercept.

x + 4y = -8


Answer1

Answer

(0, -2)

(-4, -1)

x + 4y = -8


Something to memorize

Something to Memorize

  • The graph of a horizontal line has a slope of 0 and no x-intercept.

  • The graph of a vertical line has an undefined slope and no y-intercept.


Example 7

Example 7

Graph each equation.

y = 4

y = mx + b

y = 0x + 4

No matter what the value of x, y = 4.

So, all ordered pairs are of the form (x, 4).

Some examples are (0, 4) and (-3, 4).


Example 7 continued

0

Example 7: Continued

(-3, 4)

(0, 4)


Example 8

Example 8

Graph each equation.

x = -2

Slope is undefined, y- intercept: none

No matter what the value of y, x = -2.

So, all ordered pairs are of the form (-2, y).

Some examples are (-2, -1) and (-2, 3).


Example 81

Example 8

(-2, 3)

(-2, -1)


Your turn7

Your Turn

Graph each equation.

y= -1


Answer2

y = -1

Answer


Try this one

Try This One

Graph each equation.

x = 3


Answer3

Answer

x = 3


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