Answer
$ y-13=-2(x+6) \qquad$ ... point-slope form
$y=-2x+1 \qquad$ ... slope-intercept form
$f(x)=-2x+1 \qquad$ ... function notation
Work Step by Step
$(x_{1},y_{1})=(-6,13) \; (x_{2},y_{2})=(-2,5)$
$m=\displaystyle \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{5-13}{-2-(-6)}=\frac{-8}{4}=-2$.
So with $m=-2$ and $(x_{1},y_{1})=(-6,13)$, we write the point-slope form
$y-y_{1}=m(x-x_{1})$
$ y-13=-2(x+6) \qquad$ ... point-slope form
Simplify to slope-intercept form, $ y=mx+b$
... distribute
$ y-13=-2x-12 \qquad$ ...add 13
$ y=-2x+1 \qquad$ ... is the slope-intercept form
For function notation, replace $y$ with $f(x)$.
