Answer
$f(x)=\frac{1}{3}x-7$
Work Step by Step
We are given the points $(-3,-8)$ and $(-6,-9)$. We can use the slope formula to find the slope of a line going through these points.
$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-9-(-8)}{-6-(-3)}=\frac{-1}{-3}=\frac{1}{3}$
Next, we can use this slope and one of the given points to write the line in the point slope form $y-y_{1}=m(x-x_{1})$.
$f(x)=y+8=\frac{1}{3}(x+3)=\frac{1}{3}x+1$
Subtract 8 from both sides.
$f(x)=\frac{1}{3}x-7$