Slope of a Line

Warm Up

Lesson Presentation

Problem of the Day

Lesson Quizzes

Slope of a Line

Warm Up Evaluate each equation for x = –1, 0, and 1.

1. y = 3x

2. y = x – 7

3. y = 2x + 5

4. y = 6x – 2

–3, 0, 3

–8, –7, –6

3, 5, 7

–8, –2, 4

Slope of a Line

Problem of the Day

Write a linear equation that contains terms with x2.

Possible answer: x2 + y = x2 + x + 4

Slope of a Line

Learn to find the slope of a line and use

slope to understand and draw graphs.

Slope of a Line

Vocabulary

rise

run

slope

Slope of a Line

The constant rate of change of a line is called the slope of the line.

Slope of a Line

(5, 4)

(1, 2) Then count horizontally to the second point to find the run.

Find the slope of the line.

Begin at one point and count vertically to find the rise.

Additional Example 1: Finding the Slope of a Line

slope = = 2 4

1 2

The slope of the line is . 1 2

Slope of a Line

(3, 2)

(–1, –2)

Then count horizontally to the second point to find the run.

Find the slope of the line.

Begin at one point and count vertically to find the rise.

Check It Out: Example 1

slope = = 1 4 4

The slope of the line is 1.

Slope of a Line

If you know any two points on a line, or two solutions of a linear equation, you can find the slope of the line without graphing. The slope m of a line through the points (x1, y1) and (x2, y2) is as follows:

y2 – y1 x2 – x1

m =

Slope of a Line

Find the slope of the line that passes through (–2, –3) and (4, 6).

Additional Example 2: Finding Slope, Given Two

Points

Let (x1, y1) be (–2, –3) and (x2, y2) be (4, 6).

6 – (–3) 4 – (–2)

Substitute 6 for y2, –3 for y1, 4 for x2, and –2 for x1.

9 6

=

The slope of the line that passes through

(–2, –3) and (4, 6) is . 3 2

= y2 – y1 x2 – x1

3 2

=

Slope of a Line

Find the slope of the line that passes through (–4, –6) and (2, 3).

Check It Out: Example 2

Let (x1, y1) be (–4, –6) and (x2, y2) be (2, 3).

3 – (–6) 2 – (–4)

Substitute 3 for y2, –6 for y1, 2 for x2, and –4 for x1.

9 6

=

The slope of the line that passes through

(–4, –6) and (2, 3) is . 3 2

= y2 – y1 x2 – x1

3 2

=

Slope of a Line

Additional Example 3: Money Application

The table shows the total cost of fruit per pound purchased at the grocery store. Use the data to make a graph. Find the slope of the line and explain what it shows.

Graph the data.

Pounds

Co

st

Cost of Fruit

Slope of a Line

Additional Example 3 Continued

Find the slope of the line:

The slope of the line is 3. This means that for every pound of fruit, you will pay another $3.

= y2 – y1 x2 – x1

15 5

=

30 – 15 10 – 5

= 3

Slope of a Line

Check It Out: Example 3

The table shows the total cost of gas per gallon. Use the data to make a graph. Find the slope of the line and explain what it shows.

Graph the data.

Cost of Gas

Gallons Cost

0 0

3 6

6 12

6

9

9

12

6 0

3

3 x

y

Gallons

Cost of Gas

Co

st

Slope of a Line

Check It Out: Example 3 Continued

Find the slope of the line:

The slope of the line is 2. This means that for every gallon of gas, you will pay another $2.

= y2 – y1 x2 – x1

6 3

=

12 – 6 6 – 3

= 2

Slope of a Line

Slope of a Line

Slope of a Line

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

Slope of a Line

Lesson Quiz: Part I

Find the slope of the line passing through each pair of points.

1. (4, 3) and (–1, 1)

2. (–1, 5) and (4, 2)

2 5

5 3 –

Slope of a Line

Lesson Quiz: Part II

3. The table shows how much money Susan earned as a house painter for one afternoon. Use the data to make a graph. Find the slope of the line and explain what it shows.

x

y

6 4 2 8 10 12 14 0

10

20

30

40

50

60

70

80

The slope of the line is 7. This means Susan earned $7 for each hour worked.

Slope of a Line

1. Identify the slope of the line passing through the pair of points (5, 2) and (–2, 1). A. 7 B. –3 C. D.

Lesson Quiz for Student Response Systems

Slope of a Line

2. The table shows the number of hours a student works and her earnings. Identify the slope of the line and explain what it shows. A. The slope of the line is 15. This means that the student earns $15 for every hour that she works. B. The slope of the line is 30. This means that the student earns $30 for every hour that she works.

Lesson Quiz for Student Response Systems