Answer
$f(x)=\frac{5}{4}x-13$
Work Step by Step
We are given the points $(8,-3)$ and $(4,-8)$. We can use the slope formula to find the slope of a line going through these points.
$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-8-(-3)}{4-8}=\frac{-5}{-4}=\frac{5}{4}$
Next, we can use this slope and one of the given points to write the line in the point slope form $y-y_{1}=m(x-x_{1})$.
$f(x)=y+3=\frac{5}{4}(x-8)=\frac{5}{4}x-10$
Subtract 3 from both sides.
$f(x)=\frac{5}{4}x-13$
