Answer
$y=-\frac{2}{3}x-\frac{8}{3}$
Work Step by Step
First, we find the slope as follows
$$
m=\frac{y_2-y_1}{x_2-x_1}=\frac{0+2}{-4+1}=-\frac{2}{3}
.$$
The point-slope form of a line is given as:
$$y-y_1=m(x-x_1)$$
We plug in the given point and slope and solve for $y$:
$$y-0=-\frac{2}{3}(x+4)\Longrightarrow y=-\frac{2}{3}x-\frac{8}{3}
.$$
