Section 3.4 Slope-Intercept Form of a Linear Equation 235 Determining If Two Lines Are Parallel, Perpendicular, or Neither Example 5 For each pair of lines, determine if they are parallel, perpendicular, or neither. a. b. l1: y 32 l1: y 3x 5 x 2 Solution: a. The slope of is 3. l1: y 3x 5 l1 l2: y 3x 1 l2 The slope of is 3. Because the slopes are the same, the lines are parallel. b. The slope of l1 is . The slope of l2 is . The slopes are not the same.Therefore, the lines are not parallel.The values of the slopes are reciprocals, but they are not opposite in sign. Therefore, the lines are not perpendicular. The lines are neither parallel nor perpendicular. Skill Practice For each pair of lines determine if they are parallel, perpendicular, or neither. 8. 9. y 5 6 x 1 2 y 3x 15 y 5 6 x 1 2 y 3x 5 23 l2: y 23 x 1 32 l1: y 32 x 2 l2: y 23 l2: y 3x 1 x 1 Determining If Two Lines Are Parallel, Perpendicular, or Neither Example 6 For each pair of lines, determine if they are parallel, perpendicular, or neither. a. b. l1: x 3y 9 l1: x 2 l2: 3x y 4 l2: 2y 8 Solution: a. First write the equation of each line in slope-intercept form. l1: x 3y 9 l2: 3x y 4 3y x 9 3x y 4 3y y 3x 4 3 13 y x 3 1 3 9 3 x 3 l1: y l1 13 The slope of is . The slope of is . x 3 l2: y 3x 4 l2 3 3 13 The slope of is the opposite of the reciprocal of . Therefore, the lines are perpendicular. Answers 8. Neither 9. Parallel
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