Holt CA Course 1

7-7 Finding Slope of a Line

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California StandardsCalifornia Standards

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Holt CA Course 1

7-7 Finding Slope of a Line

Warm UpEvaluate 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

Holt CA Course 1

7-7 Finding Slope of a Line

AF3.4 Plot the values of quantities whose ratios are always the same (e.g. cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities. Also covered: AF3.3.

California Standards

Holt CA Course 1

7-7 Finding Slope of a Line

Recall that lines have constant slope. For a line on the coordinate plane, slope is the following ratio:

vertical change horizontal change

change in y change in x=

Holt CA Course 1

7-7 Finding Slope of a Line

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

yy22 –– yy11 xx22 –– xx11

When finding slope using the ratio above, it does not matter which point you choose for (x1, y1) and which point you choose for (x2, y2).

slope =

Holt CA Course 1

7-7 Finding Slope of a Line

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

Additional Example 1: 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.

6 + 34 + 2=

The slope of the line that passes through (–

2, –3) and (4, 6) is . 32

=y2 – y1

x2 – x1

96=

Simplify.32=

Holt CA Course 1

7-7 Finding Slope of a Line

Find the slope of the line that passes through B. (1, 3) and (2, 1).

Additional Example 1: Finding Slope, Given Two Points

Let (x1, y1) be (1, 3) and (x2, y2) be (2, 1).

1 – 32 – 1

Substitute 1 for y2, 3 for y1, 2 for x2, and 1 for x1.

2 1=

The slope of the line that passes through

(1, 3) and (2, 1) is –2.

=y2 – y1

x2 – x1

= –2 Simplify.

Holt CA Course 1

7-7 Finding Slope of a Line

Find the slope of the line that passes through C. (3, –2) and (1, –2).

Additional Example 1: Finding Slope, Given Two Points

Let (x1, y1) be (3, –2) and (x2, y2) be (1, –2).

–2 – (–2) 1 – 3

Substitute 2 for y2, 2 for y1, 1 for x2, and 3 for x1.

2 + 2 1 – 3 =

The slope of the line that passes through

(3, –2) and (1, –2) is 0.

=y2 – y1

x2 – x1

= 0

Rewrite subtraction as addition of the opposite.

0 –2=

Holt CA Course 1

7-7 Finding Slope of a Line

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

Check It Out! Example 1

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.

96=

The slope of the line that passes through (–

4, –6) and (2, 3) is . 32

=y2 – y1

x2 – x1

32=

Holt CA Course 1

7-7 Finding Slope of a Line

Find the slope of the line that passes through B. (2, 4) and (3, 1).

Check It Out! Example 1

Let (x1, y1) be (2, 4) and (x2, y2) be (3, 1).

1 – 43 – 2

Substitute 1 for y2, 4 for y1, 3 for x2, and 2 for x1.

3 1=

The slope of the line that passes through

(2, 4) and (3, 1) is –3.

=y2 – y1

x2 – x1

= –3 Simplify.

Holt CA Course 1

7-7 Finding Slope of a Line

Find the slope of the line that passes through C. (3, –2) and (1, –4).

Check It Out! Example 1

Let (x1, y1) be (3, –2) and (x2, y2) be (1, –4).

–4 – (–2) 1 – 3

Substitute 4 for y2, 2 for y1, 1 for x2, and 3 for x1.

–4 + 2 1 – 3 =

The slope of the line that passes through

(3, –2) and (1, –4) is –2.

=y2 – y1

x2 – x1

Simplify.= 1 –2 –2=

Holt CA Course 1

7-7 Finding Slope of a LineAdditional Example 2: 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

Cost

Cost of Fruit

Holt CA Course 1

7-7 Finding Slope of a Line

You can use any two points to find the slope of the line.

Helpful Hint

Holt CA Course 1

7-7 Finding Slope of a LineAdditional Example 2 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

= 3Pounds

Cost

Cost of Fruit

Substitute

Multiply

Holt CA Course 1

7-7 Finding Slope of a LineCheck It Out! Example 2

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

Cost

Holt CA Course 1

7-7 Finding Slope of a Line

Check It Out! Example 2 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

6

9

9

12

6 0

3

3 x

y

Gallons

Cost of Gas

Cost

Substitute.

Multiply.

Holt CA Course 1

7-7 Finding Slope of a Line

The slope of a line may be positive, negative, zero, or undefined. You can tell which of these is the case by looking at the graphs of a line— you do not need to calculate the slope.

Holt CA Course 1

7-7 Finding Slope of a Line

Holt CA Course 1

7-7 Finding Slope of a Line

Holt CA Course 1

7-7 Finding Slope of a Line

Lesson Quiz: Part I

Find the slope of the line that passes through each pair of points.

1. (4, 3) and (–1, 1)

2. (–1, 5) and (4, 2)

25

53–

Holt CA Course 1

7-7 Finding Slope of a LineLesson 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

64 2 8 10 12 14 0

10

20

30

40

50

60

7080

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