To find the slope of the line that passes through the points \((2, 4)\) and \((9, 6)\), we can use the formula for the slope \(m\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, we can identify the coordinates:
- \((x_1, y_1) = (2, 4)\)
- \((x_2, y_2) = (9, 6)\)
Now, substituting the values into the slope formula:
\[ m = \frac{6 - 4}{9 - 2} = \frac{2}{7} \]
Thus, the slope of the line that passes through the points \((2, 4)\) and \((9, 6)\) is
\[ \boxed{\frac{2}{7}} \]