Find c such that (−3,−8), (−7,−6), and (c,4) lie on a line.

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