Answer
$ y+4=0(x+1) \qquad$ ... point-slope form
$y=-4 \qquad$ ... slope-intercept form
$f(x)=-4$ $\qquad$ ... function notation
Work Step by Step
$(x_{1},y_{1})=(-1,-4) \; (x_{2},y_{2})=(3,-4)$
$m=\displaystyle \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-4-(-4)}{3-(-1)}=\frac{0}{4}=0$.
So with $m=0$ and $(x_{1},y_{1})=(-1,-4)$, we write the point-slope form
$y-y_{1}=m(x-x_{1})$
$ y+4=0(x+1) \qquad$ ... point-slope form
Simplify to slope-intercept form, $ y=mx+b$
$ y+4=0 \qquad$ ...add $(-4)$
$ y=-4 \qquad$ ... is the slope-intercept form
For function notation, replace $y$ with $f(x)$.
