Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.5 - More on Slope - Exercise Set - Page 226: 21


The equation in slope-intercept form of the line perpendicular to the line $x=6$ and passing through the point $\left( -1,5 \right)$ is $y=5$.

Work Step by Step

The line $x=6$ is the vertical line. Then, this line has undefined slope. The horizontal line having zero slope is perpendicular to a vertical line having undefined slope. Thus, the slope of the line perpendicular to the line $x=6$ is 0. Substitute the value of the slope of the line $m=0$ and point $\left( {{x}_{1}},{{y}_{1}} \right)=\left( -1,5 \right)$ in the equation $y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)$. $\begin{align} & y-5=\left( 0 \right)\left( x-\left( -1 \right) \right) \\ & y-5=0 \\ & y=5 \end{align}$ Thus, the required equation of the line is $y=5$.
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