Answer
$ y+4=-\displaystyle \frac{2}{3}(x-6) \qquad$ ... point-slope form
$y=-\displaystyle \frac{2}{3}x \qquad$ ... slope-intercept form
$f(x)=-\displaystyle \frac{2}{3}x \qquad$ ... function notation
Work Step by Step
Given: $m=-\displaystyle \frac{2}{3}, \; (x_{1},y_{1})=(6,-4)$
Point-slope form:
$y-y_{1}=m(x-x_{1})$
$y-(-4)=-\displaystyle \frac{2}{3}(x-6)$
$ y+4=-\displaystyle \frac{2}{3}(x-6)\qquad$ ... point-slope form
... Simplify to slope-intercept form, $ y=mx+b$
$ y+4=-\displaystyle \frac{2}{3}x+4\qquad$... subtract 4
$ y=-\displaystyle \frac{2}{3}x \qquad$ ... is the slope-intercept form
For function notation, replace $y$ with $f(x)$.
