EXAMPLE 1 Find slopes of lines in a coordinate plane

Find the slope of line a and line d.

SOLUTION

Slope of line a: m = – 1

Slope of line d: m =4 – 0 6 – 6

= 4 0

which is undefined.

y2 – y1 x2 – x1

= = 4 – 2 6 – 8

= 2– 2

y2 – y1 x2 – x1

=

GUIDED PRACTICE for Example 1

Use the graph in Example 1. Find the slope of the line.

1. Line b

2ANSWER

GUIDED PRACTICE for Example 1

Use the graph in Example 1. Find the slope of the line.

2. Line c

0ANSWER

EXAMPLE 2 Identify parallel lines

Find the slope of each line. Which lines are parallel?

SOLUTION

Find the slope of k1 through (– 2, 4) and (– 3, 0).

= – 4 – 1 = 4

m21 – 5 3 – 4

= = 4

Find the slope of k2 through (4, 5) and (1, 3).

=– 4 – 1

m1 =0 – 4

– 3 – (– 2 )

EXAMPLE 2 Identify parallel lines

m3– 2 – 3 5 – 6

= =– 5 – 1

= 5

Find the slope of k3 through (6, 3) and (5, – 2).

Compare the slopes. Because k1 and k2 have the same slope, they are parallel. The slope of k3 is different, so k3 is not parallel to the other lines.

GUIDED PRACTICE for Example 2

3. Line m passes through (–1, 3) and (4, 1). Line t passes through (–2, –1) and (3, – 3). Are the two lines parallel? Explain how you know.

Yes; they have the same slope.

ANSWER

EXAMPLE 3 Draw a perpendicular line

SOLUTION

Line h passes through (3, 0) and (7, 6). Graph the line perpendicular to h that passes through the point (2, 5).

= 64

= 32

m1 = 6 – 0 7 – 3

STEP 1

Find the slope m1 of line h through (3, 0) and (7, 6).

EXAMPLE 3 Draw a perpendicular line

STEP 2

Find the slope m2 of a line perpendicular to h. Use the fact that the product of the slopes of two perpendicular lines is –1.

m2 =32

– 1

m2 = – 2 3

Slopes of perpendicular lines

23

Multiply each side by

STEP 3

Use the rise and run to graph the line.

GUIDED PRACTICE for Examples 3 and 4

4. Line n passes through (0, 2) and (6, 5). Line m passes through (2, 4) and (4, 0). Is n m? Explain.

ANSWER Yes; the product of their slopes is – 1.

5. In Example 4, which parachute is in the air for the longest time? Explain.

SAMPLE ANSWER

Parachute C. It was in the air approximately 1.25 minutes longer than either a or b.

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