To find the slope \( m \) of the line that passes through the points \( (x_1, y_1) = (9, 6) \) and \( (x_2, y_2) = (5, 13) \), we use the formula for the slope:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Plugging in the coordinates:
\[ m = \frac{13 - 6}{5 - 9} \]
Calculating the differences:
\[ m = \frac{7}{-4} \]
This simplifies to:
\[ m = -\frac{7}{4} \]
Therefore, the slope of the line that passes through the points \( (9, 6) \) and \( (5, 13) \) is
\[ \boxed{-\frac{7}{4}} \]