Precalculus (6th Edition) Blitzer

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

Chapter 1 - Section 1.4 - Linear Functions and Slope - Exercise Set - Page 213: 79


The value of y is $y=-2$.

Work Step by Step

Let us consider a line that passes through the given points $\left( 3,y \right)$ and $\left( 1,4 \right)$. The slope of the line is $m=-3$. The slope of a line that passes through two points $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ is as follows: $m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$ Now, put $m=-3$ , $\left( {{x}_{1}},{{y}_{1}} \right)=\left( 3,y \right)$ , and $\left( {{x}_{2}},{{y}_{2}} \right)=\left( 1,4 \right)$ And, calculate the value of $y$ as follows: $\begin{align} & -3=\frac{4-y}{1-3} \\ & -3=\frac{4-y}{\left( -2 \right)} \\ & 4-y=-3\times \left( -2 \right) \\ & 4-y=6 \end{align}$ On further simplification, we get, $\begin{align} & -y=6-4 \\ & -y=2 \\ & y=-2 \end{align}$ Therefore, the value of y is $-2$ so that the slope of the line that passes through the points $\left( 3,y \right)$ and $\left( 1,4 \right)$ is $m=-3$.
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