Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 1 - Linear Functions - 1.1 Slopes and Equations of Lines - 1.1 Exercises - Page 13: 33



Work Step by Step

Perpendicular lines have slopes that are negative reciprocals of each other. The given line has a slope of $-\frac{1}{5}$. This means that the slope of the line perpendicular to it is $5$. Thus, the tentative equation of the line is $y=5x+b$. The line is said to have a $y$-intercept of $4$ so $b=4$. Therefore the equation of the line perpendicular to the given line is $y=5x+4$ Convert this to $ax+by=c$ form to have: $y=5x+4 \\-5x+y=4 \\-1(-5x+y)=4(-1) \\5x-y=-4$
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