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. SOLUTION Find the slope of m through (– 1, 3) and (4, 1). m1 = 3 – 1 – 1 – 4 = 2 – 5 = 2 5 –
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.