Answer
The equation of the line is $y=3x-2$
Work Step by Step
$(x_{1},y_{1})=(-1,-5)$
$(x_{2},y_{2})=(1,1)$
Find the slope of the line: $m=\displaystyle \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
$m=\displaystyle \frac{1-(-5)}{1-(-1)}=\frac{6}{2}=3$
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 $(x_{1},y_{1})=(-1,-5).$
$ y-y_{1}=m(x-x_{1})\qquad$ ...substitute $-5$ for $y_{1},\ 3$ for $m$ and $-1$ for $x_{1}$.
$y-(-5)=3(x-(-1))$
$ y+5=3(x+1)\qquad$ ...apply the Distributive Property.
$ y+5=3x+3\qquad$ ...add $-5$ to each side.
$y=3x-2$
