The equation of the image line is y= -0.5x.
When a line is reflected in a certain line, in this case the original line is reflected in the line y=-2, we simply flip it to the other side with respect to the line to which it is reflected. If you are going to graph it, you can see that the distance of the original line (y= 0.5x-4) from the line to which it is reflected (y=-2) and the distance of the reflected line (y=-0.5x) are symmetric.