Answer
The equation of the line is $y=-2x$
Work Step by Step
$(x_{1},y_{1})=(-2,4)$
$(x_{2},y_{2})=(1,-2)$
Find the slope of the line: $m=\displaystyle \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
$m=\displaystyle \frac{-2-4}{1-(-2)}=\frac{-6}{3}=-2$
You know the slope and a point on the line, so use point-slope form with either
given point to write an equation of the line. Choose $(x_{1},y_{1})=(-2,4).$
$ y-y_{1}=m(x-x_{1})\qquad$ ...substitute $4$ for $y_{1},\ -2$ for $m$ and $-2$ for $x$.
$ y-4=-2(x+2)\qquad$ ...apply the Distributive Property.
$ y-4=-2x-4\qquad$ ...add $4$ to each side.
$y=-2x$
