To find the slope of the line passing through the points $(-9, -3)$ and $(7, -7)$, we can use the slope formula:

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

Where $(x_1, y_1) = (-9, -3)$ and $(x_2, y_2) = (7, -7)$.

Substituting the values:

$m = \frac{-7 - (-3)}{7 - (-9)} = \frac{-7 + 3}{7 + 9} = \frac{-4}{16} = -\frac{1}{4}$

So, the slope of the line is:

$m = -\frac{1}{4}$

Would you like further details or have any questions? Here are some related questions to expand your understanding:

1. How do you find the equation of a line once you have the slope?
2. What is the significance of a negative slope?
3. How do you interpret the slope in real-world contexts?
4. What would the slope be if the two points were swapped?
5. How does changing one of the points affect the slope?

Tip: Always double-check the sign of the coordinates when calculating the slope. A small error in signs can lead to an incorrect slope.