The equation of a line passing through the point (5, –3) and having the y-intercept of 8 units below the x-axis is:

1. x + y – 8 = 0

2. x – y – 8 = 0

3. 2x + y – 4 = 0

4. x – 2y – 8 = 0

The line intersects the y-axis 8 units below the x-axis. This means the line intersect y-axis at (0, -8).

Thus, y-intercept of lie (c) = -8

Thus, line passes through (0, -8) and (5, -3).

We know that,

$m = \dfrac{y$2 - y1}{x2 - x1} \\[1em] = \dfrac{-3 - (-8)}{5 - 0} \\[1em] = \dfrac{5}{5} \\[1em] = 1.

Substitute m = 1 and c = -8 into y = mx + c, we get :

⇒ y = 1.x + (-8)

⇒ y = x - 8

⇒ x - y - 8 = 0.

Hence, option 2 is the correct option.