Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix B - Coordinate Geometry and Lines - B Exercises: 36

Answer

$y= -2x + \frac13$

Work Step by Step

We are told to find the equation of the line that satisfies the following conditions: Passes through the point $(\frac12,-\frac23)$, and perpendicular to the line $4x -8y = 1$ To find the equation of the line we must find the slope then write it in the form:$ y =mx + b$ First solve the given equation for $y$: $4x - 8y = 1$ $-8y = -4x + 1$ $y = \frac{1}{2}x - \frac{1}{8}$ Since the lines are perpendicular the slope is the negative reciprocal, so the slope of our equation is $m = -2$ $y - (-\frac23) = -2(x-\frac12)$ $y = -2x + 1 - \frac23$ $y= -2x + \frac13$
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