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