Answer
$f(x)=-\frac{7}{6}x-\frac{4}{3}$
Work Step by Step
To find the equation of the line, we first find the slope between the points $(-2,1)$ and $(4,\ -6)$:
$m=\displaystyle \frac{-6-1}{4--2}=-\frac{7}{6}$
Next, we plug in one of the points $(-2,1)$ and the slope into the point-slope formula for a line:
$y-1=-\displaystyle \frac{7}{6}(x+2)$
$y=-\frac{7}{6}x-\frac{7*2}{6}+1$
$y=-\frac{7}{6}x-\frac{7}{3}+1$
$y=-\frac{7}{6}x-\frac{4}{3}$
