Answer
$ f(x)=-\frac{1}{2}x$
Work Step by Step
$f(-4)=2$ can be written as $(-4,2)$ and $f(6)=-3$ as $(6,-3)$
Slope $m=\frac{-3-2}{6-(-4)}=\frac{-5}{10}=-\frac{1}{2}$
Point-slope form is
$y-y_{1}=m(x-x_{1})$
Using the values of slope $m$ and point $(6,-3)$, we get
$y-(-3)=-\frac{1}{2}(x-6)$
$\implies y+3=-\frac{1}{2}x+3$
$\implies y=-\frac{1}{2}x+3-3=-\frac{1}{2}x$
A linear function is
$ f(x)=-\frac{1}{2}x$
