To find the slope of the line that passes through the points \((2, 7)\) and \((6, 6)\), we can use the formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, we assign:
- \(x_1 = 2\), \(y_1 = 7\)
- \(x_2 = 6\), \(y_2 = 6\)
Now, substitute the values into the slope formula:
\[ m = \frac{6 - 7}{6 - 2} \]
Calculating the differences:
\[ m = \frac{-1}{4} \]
Therefore, the slope of the line is
\[ \boxed{-\frac{1}{4}}. \]