242 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 0 1 1 132 m1 One slope is the opposite of the reciprocal of the other slope. Therefore, the lines are perpendicular. 4. Applications of Slope: Rate of Change In many applications, the interpretation of slope refers to the rate of change of the y value compared to the x value. 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. Source: U.S. Department of the Census Example 8 m2 1 4 m1 4 m2 1 4 m1 8 2 m2 1 172 4 2 Skill Practice Determine if lines l1 and l2 are parallel, perpendicular, or neither. 8. l1: (2, 3) and (4, 1) l2: (0, 2) and (3, 1) Skill Practice 9. In the year 2000, the population of Alaska was approximately 630,000. By 2010, it had grown to approximately 700,000. Use the ordered pairs (2000, 630000) and (2010, 700000) to determine the slope of the line through the points. Then interpret the meaning in the context of this problem. Answers 8. Parallel 9. m 7000; The population of Alaska increased at a rate of 7000 people per year. 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 Solution: To determine the slope we need to know two points on the line. From the graph, the median income for males in the year 2000 was approximately $28,300. Classroom Example: p. 246, Exercise 68 TIP: You can check that two lines are perpendicular by checking that the product of their slopes is 1. 4a 1 4b 1 Classroom Example: p. 247, Exercise 76
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