Answer
The slope-intercept form is $y=-2x$.
Work Step by Step
The given points are
$(x_1,y_1)=(-2,4)$ and $(x_2,y_2)=(0,0)$
Slope
$\Rightarrow m=\frac{y_2-y_1}{x_2-x_1}$
Substitute all the values.
$\Rightarrow m=\frac{0-4}{0-(-2)}$
Simplify.
$\Rightarrow m=\frac{-4}{2}$
$\Rightarrow m=-2$
The point-slope form
$\Rightarrow y-y_1=m(x-x_1)$
Substitute $-2$ for $m,$ $-2$ for $x_1$ and $4$ for $y_1$.
$\Rightarrow y-4=-2(x-(-2))$
$\Rightarrow y-4=-2(x+2)$
Use distributive property.
$\Rightarrow y-4=-2x-4$
Add $4$ to each side.
$\Rightarrow y-4+4=-2x-4+4$
Simplify.
$\Rightarrow y=-2x$
Hence, the slope-intercept form is $y=-2x$.
