To find the slope \( m \) of the line that passes through the points \((x_1, y_1) = (10, 8)\) and \((x_2, y_2) = (7, 6)\), we use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the coordinates of the points into the formula:
\[ m = \frac{6 - 8}{7 - 10} \]
Now, calculate the differences:
\[ m = \frac{-2}{-3} \]
Simplifying the fraction:
\[ m = \frac{2}{3} \]
Thus, the slope of the line that passes through the points \((10, 8)\) and \((7, 6)\) is
\[ \boxed{\frac{2}{3}}. \]