Answer
$f(x)= -\frac{3}{2}x-\frac{7}{2}$
Work Step by Step
$f(-9)=10$ can be written as $(-9,10)$ and $f(-1)=-2$ as $(-1,-2)$
Slope $m=\frac{-2-10}{-1-(-9)}=\frac{-12}{8}=-\frac{3}{2}$
Point-slope form is
$y-y_{1}=m(x-x_{1})$
Using the values of slope $m$ and point $(-1,-2)$, we get
$y-(-2)=-\frac{3}{2}(x-(-1))$
$\implies y+2=-\frac{3}{2}(x+1)$
$\implies y=-\frac{3}{2}x-\frac{3}{2}-2$
$\implies y= -\frac{3}{2}x-\frac{7}{2}$
A linear function is
$f(x)= -\frac{3}{2}x-\frac{7}{2}$
