Calculus 8th Edition

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

Appendix B - Coordinate Geometry and Lines - B Exercises - Page A15: 35


$y= \frac52x + \frac12$

Work Step by Step

We are told to find the equation of the line that satisfies the following conditions: Passes through the point (-1,-2), and perpendicular to the line $2x + 5y +8 = 0$ 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 $y$: $2x + 5y + 8 = 0$ $5y = -2x - 8$ $y = -\frac{2}{5}x - \frac{8}{5}$ Since the lines are perpendicular the slope is the negative reciprocal, so the slope of our equation is $m = \frac52$ $y - (-2) = \frac52(x-(-1)$ $y = \frac52x + \frac52 - 2$ $y= \frac52x + \frac12$
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