Precalculus (6th Edition) Blitzer

The value of y is $y=-2$.
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 $m=-3$.