Suppose you have two points (a, b) and (c, d).
By the slope formula, the line which passes through them will be:
(y - b) / (x - a) = (d - b) / (c - a)
Thus, using the slope formula with (-1, -7) and (-6, -3), we have:
(y + 7) / (x + 1) = (-3 + 7) / (-6 + 1)
(y + 7) / (x + 1) = 4 / -5
y + 7 = (-4/5)(x + 1)
y + 7 = (-4/5)x - 4/5
y = (-4/5)x - 4/5 - 7
y = (-4/5)x - 39/5, which is the equation of the line you need.