Answer
$y+5=0(x+2) $... point-slope form
$y=-5 \qquad$ ... slope-intercept form
$f(x)=-5$ $\qquad$ ... function notation
Work Step by Step
$(x_{1},y_{1})=(-2,-5) \; (x_{2},y_{2})=(3,-5)$
$m=\displaystyle \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-5-(-5)}{3-(-2)}=\frac{0}{5}=0$.
So with $m=0$ and $(x_{1},y_{1})=(-2,-5)$, we write the point-slope form
$y-y_{1}=m(x-x_{1})$
$ y+5=0(x+2) \qquad$ ... point-slope form
Simplify to slope-intercept form, $ y=mx+b$
$ y+5=0 \qquad$ ...add $(-8)$
$ y=-5 \qquad$ ... is the slope-intercept form
For function notation, replace $y$ with $f(x)$.
