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 –

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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. y 2 – y 1 x 2 – x 1 = = 4 – 2 6 – 8 = 2 – 2 y 2 – y 1 x 2 – x 1 =

GUIDED PRACTICE for Example 1 Use the graph in Example 1. Find the slope of the line. 1. Line b 2 ANSWER

GUIDED PRACTICE for Example 1 Use the graph in Example 1. Find the slope of the line. 2. Line c 0 ANSWER

EXAMPLE 2 Identify parallel lines Find the slope of each line. Which lines are parallel? SOLUTION Find the slope of k 1 through (– 2, 4) and (– 3, 0). = – 4 – 1 = 4 m2m2 1 – 5 3 – 4 = = 4 Find the slope of k 2 through (4, 5) and (1, 3). = – 4 – 1 m1m1 = 0 – 4 – 3 – (– 2 )

EXAMPLE 2 Identify parallel lines m3m3 – 2 – 3 5 – 6 = = – 5 – 1 = 5 Find the slope of k 3 through (6, 3) and (5, – 2). Compare the slopes. Because k 1 and k 2 have the same slope, they are parallel. The slope of k 3 is different, so k 3 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). = 6 4 = 3 2 m1m1 = 6 – 0 7 – 3 STEP 1 Find the slope m 1 of line h through (3, 0) and (7, 6).

EXAMPLE 3 Draw a perpendicular line STEP 2 Find the slope m 2 of a line perpendicular to h. Use the fact that the product of the slopes of two perpendicular lines is –1. m2m2 = 3 2 – 1 m2m2 = – 2 3 Slopes of perpendicular lines 2 3 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. ANSWERYes; the product of their slopes is – 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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