Property Perpendicular Lines When neither line is vertical, perpendicular lines have slopes that are negative reciprocals of each other. EXAMPLE 5 Determine whether each pair of line is parallel, perpendicular, or neither. a) 3x 6y 10 b) 2x 7y 7 c) y 7x 4 x 2y 12 21x 6y 2 7x y 9 Solution a) To determine if the lines are parallel or perpendicular, we must fi nd the slope of each line. Write each equation in slope-intercept form. 3x 6y 10 6y 3x 10 y y m Each line has a slope of 1 2 3 6 x 10 6 1 2 x 5 3 1 2 x 2y 12 2y x 12 y x 2 12 2 y 1 2 x 6 m 1 2 . Their y-intercepts are different. Therefore, 3x 6y 10 and x 2y 12 are parallel lines. b) Begin by writing each equation in slope-intercept form so that we can fi nd their slopes. 2x 7y 7 7y 2x 7 y 2 7 x 7 7 y 2 7 x 1 m 2 7 21x 6y 2 6y 21x 2 y 21 6 x 2 6 y 7 2 x 1 3 m 7 2 The slopes are negative reciprocals, therefore the lines are perpendicular. c) Again, we must fi nd the slope of each line. y 7x 4 is already in slope- intercept form. Its slope is 7. Write 7x y 9 in slope-intercept form. y 7x 9 Add 7x to each side. y 7 1 x 9 1 Divide by 1. y 7x 9 Simplify. m 7 The slope of y 7x 4 is 7. The slope of 7x y 9 is 7. Since the slopes are different and not negative reciprocals, these lines are not parallel, and they are not perpendicular. www.mhhe.com/messersmith SECTION 4.3 Writing an Equation of a Line 177
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