Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 8 - Coordinate Geometry and Linear Systems - 8.4 - Writing Equations of Lines - Problem Set 8.4: 59

Answer

$ 3x + 2y =0 $

Work Step by Step

First, we solve for the slope of the perpendicular line: $-2x + 3y = 8 \\ 3y = 2x+8 \\ y = 2/3 x +8/3$ Since this is in slope intercept form, we see that the slope is 2/3. Thus, the slope of the perpendicular line is the opposite reciprocal, which is -3/2. Thus, we use point slope form, and then we simplify to standard form: $y - y_{1} = m(x-x_{1}) \\ y = -3/2(x) \\ 2y = -3x \\ 3x+2y=0$
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