Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 2 - Section 2.5 - The Point-Slope Form of the Equation of a Line - Exercise Set - Page 164: 66

Answer

$\frac{B}{A}$.

Work Step by Step

The given equation of the line is $\Rightarrow Ax+By=C$ Isolate $y$. Subtract $Ax$ from both sides. $\Rightarrow Ax+By-Ax=C-Ax$ Simplify. $\Rightarrow By=C-Ax$ Divide both sides by $B$. $\Rightarrow \frac{By}{B}=\frac{C-Ax}{B}$ Simplify. $\Rightarrow y=\frac{C}{B}-\frac{Ax}{B}$ $\Rightarrow y=-\frac{A}{B}x+\frac{C}{B}$ This is in the slope-intercept form. $\Rightarrow y=mx+c$ Where slope of the line is $m=-\frac{A}{B}$. Two lines are perpendicular if their slopes are negative reciprocal to each other. Hence, the slope of the perpendicular line is $=−\frac{1}{m}$ $=−\frac{1}{-\frac{A}{B}}$ Simplify. $=\frac{B}{A}$.
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