224 Chapter 3 Graphing Linear Equations in Two Variables If the slopes of two lines are known, then we can compare the slopes to determine if the lines are parallel, perpendicular, or neither. Determining If Lines Are Parallel, Perpendicular, or Neither Example 7 Lines l1 and l2 pass through the given points. Determine if l1 and l2 are parallel, perpendicular, or neither. l1: (2,7) and (4, 1) l2: (3, 1) and (1, 0) l1: (2,7) and (4, 1) l2: (3, 1) and (1, 0) 1x1, y12 1x2, y22 1x1, y12 1x2, y22 One slope is the opposite of the reciprocal of the other slope.Therefore, the lines are perpendicular. Skill Practice Determine if lines l1 and l2 are parallel, perpendicular, or neither. 8. l1: 12,32 and 14,12 4. Applications of Slope: Rate of Change In many applications, the interpretation of slope refers to the rate of change of the y-variable to the x-variable. Interpreting Slope in an Application The annual median income for males in the United States for selected years is shown in Figure 3-25. The trend is approximately linear. Find the slope of the line and interpret the meaning of the slope in the context of the problem. Median Income for U.S. Males Figure 3-25 Solution: Find the slope of each line. l2: 10, 22 and 13, 12 Source: U.S. Department of the Census Example 8 m2 1 4 m1 4 m2 1 4 m1 8 2 m2 0 1 1 132 m1 1 172 4 2 Answer 8. Parallel y x 40,000 35,000 30,000 25,000 20,000 15,000 10,000 0 2000 2002 2004 2006 2008 2010 2012 Income ($) Year 35,300 5,000 28,300 TIP: You can check that two lines are perpendicular by checking that the product of their slopes is 1. 4a 1 4 b 1
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