Using the slope formula, we have:
(y - (-4)) / (x - 3) = (-5 - (-4)) / (-1 - 3)
(y + 4) / (x - 3) = -1 / -4
(y + 4) / (x - 3) = 1/4
(y + 4) = (1/4)(x - 3)
y + 4 = (1/4)x - (3/4)
y = (1/4)x - (3/4) - 4
y = (1/4)x - (19/4), which is the equation you need.