To find the slope \( m \) of the line that passes through the points \((x_1, y_1) = (10, 2)\) and \((x_2, y_2) = (2, 1)\), we use the formula for the slope:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the values from the points:
\[ m = \frac{1 - 2}{2 - 10} \]
Now, calculate the numerator and the denominator:
\[ m = \frac{-1}{-8} \]
Simplifying the fraction:
\[ m = \frac{1}{8} \]
Thus, the slope of the line that passes through the points \((10, 2)\) and \((2, 1)\) is
\[ \boxed{\frac{1}{8}}. \]