Answer
The slope-intercept form is $y=5x-2$.
Work Step by Step
The given points are
$(x_1,y_1)=(1,3)$ and $(x_2,y_2)=(0,-2)$
Slope
$\Rightarrow m=\frac{y_2-y_1}{x_2-x_1}$
Substitute all the values.
$\Rightarrow m=\frac{-2-3}{0-1}$
Simplify.
$\Rightarrow m=\frac{-5}{-1}$
$\Rightarrow m=5$
The point-slope form
$\Rightarrow y-y_1=m(x-x_1)$
Substitute $5$ for $m,$ $1$ for $x_1$ and $3$ for $y_1$.
$\Rightarrow y-3=5(x-1)$
Use distributive property.
$\Rightarrow y-3=5x-5$
Add $3$ to each side.
$\Rightarrow y-3+3=5x-5+3$
Simplify.
$\Rightarrow y=5x-2$
Hence, the slope-intercept form is $y=5x-2$.
