## Precalculus (6th Edition) Blitzer

The linear equation in slope-intercept form is $y=-3x+10$.
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 $y=-3x+10$.