Answer
$ y+4=-\displaystyle \frac{2}{5}(x-15) \qquad$ ... point-slope form
$y=-\displaystyle \frac{2}{5}x+2 \qquad$ ... slope-intercept form
$f(x)=-\displaystyle \frac{2}{5}x+2 \qquad$ ... function notation
Work Step by Step
Given: $m=-\displaystyle \frac{2}{5}, \; (x_{1},y_{1})=(15,-4)$
Point-slope form:
$y-y_{1}=m(x-x_{1})$
$y-(-4)=-\displaystyle \frac{2}{5}(x-15)$
$ y+4=-\displaystyle \frac{2}{5}(x-15)\qquad$ ... point-slope form
Simplify to slope-intercept form, $ y=mx+b$
$ y+4=-\displaystyle \frac{2}{5}x+6\qquad$... subtract 4
$ y=-\displaystyle \frac{2}{5}x+2 \qquad$ ... is the slope-intercept form
For function notation, replace $y$ with $f(x)$.
