Answer
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 $m=-3$.
