Precalculus (6th Edition) Blitzer

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

Chapter 7 - Cumulative Review Exercises - Page 880: 31


The linear equation in slope-intercept form is $y=-3x+10$.

Work Step by Step

We have the equation of the line that passes through the points $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ as given below, $ y-{{y}_{1}}=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\left( x-{{x}_{1}} \right)$ Therefore, the coordinates are given $\left( {{x}_{1}},{{y}_{1}} \right)$ as $\left( 2,4 \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ as $\left( 4,-2 \right)$. So, write the equation of the line written as follows: $\begin{align} & y-{{y}_{1}}=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\left( x-{{x}_{1}} \right) \\ & y-4=\frac{-2-4}{4-2}\left( x-2 \right) \\ & y-4=-3\left( x-2 \right) \\ & y=-3x+10 \end{align}$ Thus, the linear equation in slope-intercept form is $ y=-3x+10$.
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