College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 5 - Section 5.1 - Polynomial Functions and Models - 5.1 Assess Your Understanding - Page 342: 134

Answer

The equation of the perpendicular line is $y=-\frac{2}{5}x-\frac{11}{5}$

Work Step by Step

First, let's rearrange the line in the form y=mx+b: $5x-2y=6$ $-2y=-5x+6$ $-2y/(-2)=(-5x+6)/(-2)$ $y=\frac{5}{2}x-3$ The slope of a perpendicular line is the negative inverse: $\frac{5}{2} \rightarrow -\frac{2}{5}$ Now that we have the slope and a point, we can find the equation of the perpendicular line by first finding the y-intercept (b): $-3=-\frac{2}{5}(2)+b$ $-3=-\frac{4}{5}+b$ $-3+\frac{4}{5}=-\frac{4}{5}+b+\frac{4}{5}$ $-\frac{15}{5}+\frac{4}{5}=b$ $b=-\frac{11}{5}$ So, the equation of the perpendicular line is $y=-\frac{2}{5}x-\frac{11}{5}$
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