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