Answer
The linear equation in slope-intercept form is $y=-3x+10$.
Work Step by Step
We have the equation of the line that passes through the points $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ as given below,
$ y-{{y}_{1}}=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\left( x-{{x}_{1}} \right)$
Therefore, the coordinates are given $\left( {{x}_{1}},{{y}_{1}} \right)$ as $\left( 2,4 \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ as $\left( 4,-2 \right)$.
So, write the equation of the line written as follows:
$\begin{align}
& y-{{y}_{1}}=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\left( x-{{x}_{1}} \right) \\
& y-4=\frac{-2-4}{4-2}\left( x-2 \right) \\
& y-4=-3\left( x-2 \right) \\
& y=-3x+10
\end{align}$
Thus, the linear equation in slope-intercept form is $ y=-3x+10$.
