To find the slope \( m \) of the line that passes through the points \( (x_1, y_1) = (2, 8) \) and \( (x_2, y_2) = (5, 6) \), we can use the formula for the slope:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting in the coordinates of the points:
\[ m = \frac{6 - 8}{5 - 2} \]
Now, perform the calculations in the numerator and the denominator:
\[ m = \frac{-2}{3} \]
Thus, the slope of the line that passes through the points \( (2, 8) \) and \( (5, 6) \) is
\[ \boxed{-\frac{2}{3}} \]