EXAMPLE 1 Find slopes of lines in a coordinate plane

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