y = (-4/3)x - 1 has slope -4/3.
Thus, the line parallel to it will also slope -4/3.
Using the slope formula, we have:
(y - 1) / (x + 3) = -4/3
y - 1 = (-4/3)(x + 3)
y - 1 = (-4/3)x - 4
y = (-4/3)x - 4 + 1
y = (-4/3)x - 3, which is the equation we need.