Answer
$ y-0=2(x-3) \qquad$ ... point-slope form
$y=2x-6 \qquad$ ... slope-intercept form
$f(x)=2x-6 \qquad$ ... function notation
Work Step by Step
$(x_{1},y_{1})=(7,8) \; (x_{2},y_{2})=(3,0)\quad$ (the x-intercept)
$m=\displaystyle \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{0-8}{3-7}=\frac{-8}{-4}=2$.
So with $m=2$ and $(x_{1},y_{1})=(3,0)$, we write the point-slope form
$y-y_{1}=m(x-x_{1})$
$ y-0=2(x-3) \qquad$ ... point-slope form
Simplify to slope-intercept form, $ y=mx+b$
$ y=2x-6 \qquad$ ... is the slope-intercept form
For function notation, replace $y$ with $f(x)$.
