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: 58

Answer

$4x-y = -5$

Work Step by Step

First, we solve for the slope of the perpendicular line: $x+4y = 6 \\ y = -1/4 x - 3/2$ Since this is in slope intercept form, we see that the slope is -1/4. Thus, the slope of the perpendicular line is the opposite reciprocal, which is 4. Thus, we use point slope form, and then we simplify to standard form: $y - y_{1} = m(x-x_{1}) \\y+3 = 4(x+2) \\ y + 3 = 4x +8 \\ 4x -y = -5 $
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