To find the slope of the line that passes through the points \((7, 4)\) and \((1, 9)\), we can use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, \((x_1, y_1) = (7, 4)\) and \((x_2, y_2) = (1, 9)\). Plugging in the values:
\[ m = \frac{9 - 4}{1 - 7} \]
Calculating the differences:
\[ m = \frac{5}{1 - 7} = \frac{5}{-6} = -\frac{5}{6} \]
Thus, the slope of the line that passes through the points \((7, 4)\) and \((1, 9)\) is
\[ \boxed{-\frac{5}{6}} \]