Answer
The equation of the line is $y=-\displaystyle \frac{2}{3}x+1$
Work Step by Step
$(x_{1},y_{1})=(3,-1)$
$(x_{2},y_{2})=(6,-3)$
Find the slope of the line: $m=\displaystyle \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
$m=\displaystyle \frac{-3-(-1)}{6-3}=-\frac{2}{3}$
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 $(x_{1},y_{1})=(3,-1).$
$ y-y_{1}=m(x-x_{1})\qquad$ ...substitute $-1$ for $y_{1},\ -\displaystyle \frac{2}{3}$ for $m$ and $3$ for $x$.
$ y-(-1)=-\displaystyle \frac{2}{3}(x-3)\qquad$ ...apply the Distributive Property.
$ y+1=-\displaystyle \frac{2}{3}x+2\qquad$ ...add $-1$ to each side.
$y=-\displaystyle \frac{2}{3}x+1$
