258 CHAPTER 2 Graphs and Functions We can use a graphing calculator to support the results of Example 6. In Figure 49(a), we graph the equations of the parallel lines y1 = - 2 5 x + 4 5 and y2 = - 2 5 x + 31 5 . See Example 6(a). The lines appear to be parallel, giving visual support for our result. We must use caution, however, when viewing such graphs, as the limited resolution of a graphing calculator screen may cause two lines to appear to be parallel even when they are not. For example, Figure 49(b) shows the graphs of the equations y1 = 2x + 6 and y2 = 2.01x - 3 in the standard viewing window, and they appear to be parallel. This is not the case, however, because their slopes, 2 and 2.01, are different. Figure 49 −10 −10 10 10 y1 = − x + 2 5 4 5 y2 = − x + 2 5 31 5 These lines are parallel. (a) y1 = 2x + 6 −10 10 10 −10 y2 = 2.01x − 3 These lines are not parallel. (b) Now we graph the equations of the perpendicular lines y1 = - 2 5 x + 4 5 and y2 = 5 2 x - 5 2 . See Example 6(b). If we use the standard viewing window, the lines do not appear to be perpendicular. See Figure 50(a). To obtain the correct perspective, we must use a square viewing window, as in Figure 50(b). Figure 50 7 −10 −10 10 10 y1 = − x + 2 5 4 5 y2 = x − 5 2 5 2 A standard window (a) −10 −16.1 10 16.1 y1 = − x + 2 5 4 5 y2 = x − 5 2 5 2 A square window (b)
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