Precalculus (6th Edition) Blitzer

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

Chapter 10 - Cumulative Review Exercises - Page 1128: 37


The linear function in slope-intercept form is $ y=-5x-2$.

Work Step by Step

Let us consider the coordinates $\left( 0,-2 \right)$ as $\left( {{x}_{1}},{{y}_{1}} \right)$. We have to find the value of the slope of the equation $ x-5y-20=0$: $\begin{align} & x-5y-20=0 \\ & x-20=5y \\ & y=\frac{x}{5}-\frac{20}{5} \end{align}$ And compare this equation with the form $ y=mx+c $ to get $ m=\frac{1}{5}$. Here, ${{m}_{1}}$ is the slope of the required line that is perpendicular to $ x-5y-20=0$. And for the perpendicular lines, the condition of the slope is $ m\cdot {{m}_{1}}=-1$. So, $\begin{align} & {{m}_{1}}=\frac{-1}{m} \\ & =\frac{-1}{\frac{1}{5}} \\ & =-5 \end{align}$ Then, for the equation of the function to be determined: $\begin{align} & \frac{y-{{y}_{1}}}{x-{{x}_{1}}}={{m}_{1}} \\ & \frac{y-\left( -2 \right)}{x-0}=-5 \\ & \frac{y+2}{x}=-5 \end{align}$ And simplify it further, to get $\begin{align} & y+2=-5x \\ & y=-5x-2 \\ \end{align}$ Thus, the slope-intercept form is $ y=-5x-2$.
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