Answer
The value of y is\[-2\]
Work Step by Step
Use the formula,\[m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\]where m is slope of the line passing through points \[\left( {{x}_{1}},{{y}_{1}} \right)\]and\[\left( {{x}_{2}},{{y}_{2}} \right)\].
Take \[\left( {{x}_{1}},{{y}_{1}} \right)=\left( 3,y \right)\]and \[\left( {{x}_{2}},{{y}_{2}} \right)=\left( 1,4 \right)\], \[m=-3\].
Slope of the line is,
\[\begin{align}
& m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \\
& m=\frac{4-y}{1-3} \\
& -3=\frac{4-y}{-2}
\end{align}\]
Apply cross-products principle,
\[\begin{align}
& \left( -3 \right)\left( -2 \right)=4-y \\
& 6=4-y \\
& y=4-6 \\
& y=-2
\end{align}\]
Therefore, the value of y is, \[-2\].
Hence, the value of yfor the provided line is,\[-2\].
