# Chapter 1 - Section 1.4 - Linear Functions and Slope - Exercise Set - Page 213: 80

The value of y is $y=-6$.

#### Work Step by Step

Consider a line passing through the points $\left( -2,y \right)$ and $\left( 4,-4 \right)$. The slope of the line is $m=\frac{1}{3}$. The slope of a straight line that passes through the points $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ is as follows: $m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$ Substitute $m=\frac{1}{3}$, $\left( {{x}_{1}},{{y}_{1}} \right)=\left( -2,y \right)$, and $\left( {{x}_{2}},{{y}_{2}} \right)=\left( 4,-4 \right)$ and get the value of y as follows: \begin{align} & \frac{1}{3}=\frac{\left( -4 \right)-y}{4-\left( -2 \right)} \\ & \frac{1}{3}=\frac{-4-y}{4+2} \\ & -4-y=\frac{1}{3}\times 6 \\ & -4-y=2 \end{align} Simplify further: \begin{align} & -y=2+4 \\ & -y=6 \\ & y=-6 \end{align} Therefore, the value of y is $-6$ so that the slope of the line passing through points $\left( -2,y \right)$ and $\left( 4,-4 \right)$ is $m=\frac{1}{3}$.

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