To determine the slope of the line passing through the points $(4, -8)$ and $(-4, 4)$, we use the slope formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where:

• $(x_1, y_1) = (4, -8)$
• $(x_2, y_2) = (-4, 4)$

Substituting the values:

$m = \frac{4 - (-8)}{-4 - 4} = \frac{4 + 8}{-8} = \frac{12}{-8} = -\frac{3}{2}$

Thus, the slope of the line is:

$m = -\frac{3}{2}$

Would you like more details or have any further questions?

Here are five related questions to explore further:

1. How do you find the equation of the line given two points?
2. What does a negative slope indicate about the line's direction?
3. How do you calculate the midpoint of the line segment between two points?
4. Can you find the distance between the points $(4, -8)$ and $(-4, 4)$?
5. What are parallel and perpendicular slopes in terms of relationships?

Tip: Remember, a negative slope means the line is decreasing from left to right.