To find the slope of the line that passes through the points (1, 6) and (3, 5), we can use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
where \((x_1, y_1) = (1, 6)\) and \((x_2, y_2) = (3, 5)\).
Now, substituting the coordinates into the formula:
\[ m = \frac{5 - 6}{3 - 1} \]
Calculating the differences in the numerator and the denominator:
\[ m = \frac{-1}{2} \]
Thus, the slope of the line that passes through the points (1, 6) and (3, 5) is
\[ \boxed{-\frac{1}{2}}. \]