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Section 2.2 Slope of a Line and Rate of Change 151 Answer 8. Parallel L1: 12, 32 1L2: 15, 62 3, 22 1L1: 12, 32 L2: 15, 62 3, 22 1x2, y21x1, y1 2 1x2, y2 2 1x1, y1 2 2 L1: 1 2 12 L1 L2 . 4. Applications and Interpretation of Slope In applications, the slope of a line represents a rate of change between the y variable and the x variable. For example, a hiker walking up a hill with a slope of means that 1 ft of elevation is gained for every 6 ft traveled horizontally. Using this rate of change, we can also say that a hiker gains 10 ft of elevation for 60 ft traveled horizontally. See Figure 2-21. 16 Interpreting the Slope of a Line in an Application Example 8 The number of males 20 yr old or older who were employed full-time in the United States has grown linearly since 1970. Approximately 43.0 million males 20 yr old or older were employed full-time in 1970. By 2010, this number had grown to 69.0 million (Figure 2-22). 60 ft 6 ft 1 ft 10 ft Figure 2-21 Determining Whether Two Lines Are Parallel, Perpendicular, or Neither Two points are given from each of two lines: and Without graphing the points, determine if the lines are parallel, perpendicular, or neither. and 14, 12 and Solution: First determine the slope of each line. Then compare the values of the slopes to determine if the lines are parallel or perpendicular. For line 1: For line 2: and 14, 12 and Label the points. Apply the slope formula. The slope of is 2. The slope of is The slope of is the opposite of the reciprocal of By comparing the slopes, the lines must be perpendicular. Skill Practice Two points are given for lines and Determine if the lines are parallel, perpendicular, or neither. 8. (4,1) and (3, 6) L2: (1, 3) and (2, 0) L1 L2. L2. L1 2 4 8 4 2 m 2 162 3 5 m 1 132 4 2 L1 L2. Example 7 TIP: You can also verify that the lines in Example 7 are perpendicular by noting that the product of their slopes is 1. 2 a 1 2 b 1


miller_intermediate_algebra_4e_ch1_3
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