To find the slope of the line that passes through the points \((2, 6)\) and \((7, 0)\), you can use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Where \((x_1, y_1) = (2, 6)\) and \((x_2, y_2) = (7, 0)\).
Substituting the values into the formula:
\[ m = \frac{0 - 6}{7 - 2} \]
This simplifies to:
\[ m = \frac{-6}{5} \]
So, the slope of the line that passes through the points \((2, 6)\) and \((7, 0)\) is
\[ \boxed{-\frac{6}{5}}. \]