To find the slope \( m \) of the line that passes through the two points \( (x_1, y_1) = (6, 10) \) and \( (x_2, y_2) = (9, 6) \), we can use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting in the values from the points:
\[ m = \frac{6 - 10}{9 - 6} \]
Calculating the differences in the numerator and denominator:
\[ m = \frac{-4}{3} \]
Thus, the slope of the line that passes through the points (6, 10) and (9, 6) is
\[ \boxed{-\frac{4}{3}}. \]