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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
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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.
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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. SOLUTION Find the slope of m through (– 1, 3) and (4, 1). m1 = 3 – 1 – 1 – 4 = 2 – 5 = 2 5 –
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GUIDED PRACTICE for Example 2 Find the slope of t passes through (– 2, – 1) and (1, – 3). m2 – 1 – (– 3 ) –2 – 3 = = 2 – 5 = 2 5 – Compare the slopes. Because m and t have the same slope, they are parallel.
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