To find the slope of the line passing through the points \((-9, -3)\) and \((7, -7)\), we can use the formula for the slope \( m \), given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, \((x_1, y_1) = (-9, -3)\) and \((x_2, y_2) = (7, -7)\). Plugging in the values:
\[ m = \frac{-7 - (-3)}{7 - (-9)} \]
This simplifies to:
\[ m = \frac{-7 + 3}{7 + 9} = \frac{-4}{16} \]
Now, simplifying \(-\frac{4}{16}\):
\[ m = -\frac{1}{4} \]
Thus, the slope of the line passing through the points \((-9, -3)\) and \((7, -7)\) is:
\[ \boxed{-\frac{1}{4}} \]