To find the slope of the line that passes through the points $(8, -8)$ and $(5, -12)$, we use the slope formula:

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

Here:

• $(x_1, y_1) = (8, -8)$
• $(x_2, y_2) = (5, -12)$

Substituting the values into the formula:

$m = \frac{-12 - (-8)}{5 - 8} = \frac{-12 + 8}{5 - 8} = \frac{-4}{-3} = \frac{4}{3}$

So, the slope of the line is:

$\boxed{\frac{4}{3}}$

Would you like more details or have any questions about this solution?

Here are some related questions for further exploration:

1. How do you find the equation of a line given two points?
2. What is the significance of the slope in terms of a line's steepness and direction?
3. How do you calculate the y-intercept once the slope is known?
4. What does a negative slope indicate about a line's direction?
5. How do you apply the slope-intercept form to write the equation of a line?

Tip: Always ensure that you simplify your fractions when calculating slope to avoid errors in interpretation.