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