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: 26


The slope-intercept form of line is\[f\left( x \right)=-\frac{1}{4}x-6\]

Work Step by Step

Consider the equation $4x-y-6=0$. Isolate y terms on one side. $\begin{align} & 4x-y-6=0 \\ & -y=-4x+6 \end{align}$ Divide both sides of the equation by $-1$ to remove the negative sign. $\begin{align} & -\frac{y}{-1}=\frac{-4x+6}{-1} \\ & y=4x-6 \end{align}$ Hence, the slope ${{m}_{1}}$ of the line $4x-y-6=0$ is ${{m}_{1}}=4$ and the y-intercept is $-6$. Now, let the slope of the line $f$ be ${{m}_{2}}$. So, $\begin{align} & {{m}_{1}}\cdot {{m}_{2}}=-1 \\ & 4\cdot {{m}_{2}}=-1 \\ & {{m}_{2}}=-1\left( \frac{1}{4} \right) \\ & {{m}_{2}}=-\frac{1}{4} \end{align}$ The y-intercept is equal -- that is, $\left( 0,-6 \right)$. Now, the equation of $f$ having point $\left( 0,-6 \right)$ and slope $-\frac{1}{4}$ is: $\begin{align} & f\left( x \right)=mx+b \\ & =-\frac{1}{4}\left( x \right)+\left( -6 \right) \\ & =-\frac{1}{4}x-6 \end{align}$ Hence, the equation of the line in slope intercept form of the line which is perpendicular to the line $4x-y-6=0$ and has the same y intercept is $f\left( x \right)=-\frac{1}{4}x-6$.
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