If the 3 points are collinear, then the slopes of all line segments connecting the points are the same.
Thus,
-6 - (-8) 2
m = ------------- = -------- = -1/2
-7 - (-3) -4
Then the following must be true:
4-(-6) 10
-1/2 = ------------ = ---------
c - (-7) c + 7
Cross multiplying, -(c+7) = 20, and c+7 = -20, so that c = -27
