EXAMPLE 1 Find slopes of lines in a coordinate plane

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Presentation transcript:

EXAMPLE 1 Find slopes of lines in a coordinate plane Find the slope of line a and line d. SOLUTION y2 – y1 x2 – x1 = = 4 – 2 6 – 8 = 2 – 2 Slope of line a: m = – 1 y2 – y1 x2 – x1 = = 4 – 0 6 – 6 = 4 Slope of line d: m which is undefined.

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

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

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). m1 = 0 – 4 – 3 – (– 2 ) = – 4 – 1 = 4 Find the slope of k2 through (4, 5) and (1, 3). m2 1 – 5 3 – 4 = = – 4 – 1 = 4

EXAMPLE 2 Identify parallel lines Find the slope of k3 through (6, 3) and (5, – 2). m3 – 2 – 3 5 – 6 = = – 5 – 1 5 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 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 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 m1 of line h through (3, 0) and (7, 6). m1 = 6 – 0 7 – 3 = 6 4 = 3 2

Draw a perpendicular line 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 = 3 2 – 1 Slopes of perpendicular lines m2 = – 2 3 2 3 Multiply each side by STEP 3 Use the rise and run to graph the line.

EXAMPLE 4 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. The correct answer is D. ANSWER

GUIDED PRACTICE 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. 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.

GUIDED PRACTICE for Examples 3 and 4 In Example 4, what do the x-intercepts 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.