WarmUp 1 Exercises EXAMPLE Find slopes of lines

Warm-Up 1 Exercises EXAMPLE Find slopes of lines in a coordinate plane Find the slope of line a and line d. SOLUTION y 2 – y 1 4 – 2 2 Slope of line a: m= = = x 2 – x 1 6 – 8 – 2 = – 1 y 2 – y 1 4 – 0 Slope of line d: m = x – x = = 2 1 6– 6 4 0 which is undefined.

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

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

Warm-Up 2 Exercises EXAMPLE 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). m 1 = 0– 4 = –– 41 = 4 – 3 – (– 2 ) Find the slope of k 2 through (4, 5) and (1, 3). m 2 = 1 – 5 3– 4 = – 1 = 4

Warm-Up 2 Exercises EXAMPLE Identify parallel lines Find the slope of k 3 through (6, 3) and (5, – 2). m 3 = – 2 – 3 5– 6 – 5 = – 1 = 5 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.

Warm-Up Exercises GUIDED PRACTICE 3. for Example 2 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. ANSWER Yes; they have the same slope.

Warm-Up 3 Exercises EXAMPLE Draw a perpendicular line Line h passes through (3, 0) and (7, 6). Graph the line perpendicular to h that passes through the point (2, 5). SOLUTION STEP 1 Find the slope m 1 of line h through (3, 0) and (7, 6). m 1 = 6 – 0 = 6 = 3 7– 3 4 2

Warm-Up 3 Exercises EXAMPLE 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. 3 2 m 2 = – 1 m 2 = – 2 3 STEP 3 Slopes of perpendicular lines Multiply each side by 2 3 Use the rise and run to graph the line.

Warm-Up 4 Exercises EXAMPLE Standardized Test Practice SOLUTION The rate at which the skydiver descended is represented by the slope of the segments. The segments that have the same slope are a and c. ANSWER The correct answer is D.

Warm-Up Exercises GUIDED PRACTICE 4. for Examples 3 and 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.

Warm-Up Exercises GUIDED PRACTICE 6. for Examples 3 and 4 In Example 4, what do the xintercepts represent in the situation? How can you use this to eliminate one of the choices? SAMPLE ANSWER Time of the landing. b and c are in the air different amounts of time.