Section 3.3 Slope of a Line and Rate of Change 223 3. Parallel and Perpendicular Lines Lines in the same plane that do not intersect are called parallel lines. Parallel lines have the same slope and different y-intercepts (Figure 3-23). Lines that intersect at a right angle are perpendicular lines. If two lines are perpendicular then the slope of one line is the opposite of the reciprocal of the slope of the other line (provided neither line is vertical) (Figure 3-24). 5 4 y 3 2 1 m2 53 m1 53 5 54 3 1 2 3 4 5 21 1 2 3 4 5 x 5 3 3 5 4 y 1 54 3 1 2 3 4 5 21 1 2 3 4 5 Figure 3-23 Figure 3-24 x 3 2 m2 14 4 1 1 m1 4 4 Slopes of Parallel Lines If and represent the slopes of two parallel (nonvertical) lines, then m1 m2 See Figure 3-23. m1 m2. Slopes of Perpendicular Lines If and represent the slopes of two perpendicular lines, then m1 0 m2 0 1 m2 m1 m1m2 1. or equivalently, See Figure 3-24. Determining the Slope of Parallel and Perpendicular Lines Example 6 Suppose a given line has a slope of 6. a. Find the slope of a line parallel to the line with the given slope. b. Find the slope of a line perpendicular to the line with the given slope. Solution: a. Parallel lines must have the same slope.The slope of a line parallel to the given line is m 6. b. For perpendicular lines, the slope of one line must be the opposite of the reciprocal of the other.The slope of a line perpendicular to the given line is 53 m 16 . Skill Practice A given line has a slope of . 6. Find the slope of a line parallel to the given line. 7. Find the slope of a line perpendicular to the given line. Answers 6. 7. 3 5 5 3
miller_beginning_intermediate_algebra_4e_ch1_3
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