Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - Chapter Review Exercises - Page 36: 22


$$ y=-\frac{1}{4}x+\frac{19}{4}.$$

Work Step by Step

Since the line is perpendicular to the line given by $ y = 4x + 2$ then its slope is $-\frac{1}{4}$, and hence the line has the equation $$ y=-\frac{1}{4}x+c.$$ To find $ c $, we make use of the fact that the line passes through $(3,4)$: $$4=-\frac{1}{4}(3)+c\Longrightarrow c=\frac{19}{4}$$ Hence the equation of the line is $$ y=-\frac{1}{4}x+\frac{19}{4}.$$
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