To find the slope of the line that passes through the points \((10, 7)\) and \((6, 2)\), we use the formula for the slope \(m\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Assigning the coordinates:
- \( (x_1, y_1) = (10, 7) \)
- \( (x_2, y_2) = (6, 2) \)
We can substitute these values into the formula:
\[ m = \frac{2 - 7}{6 - 10} \]
Calculating the numerator and the denominator:
\[ m = \frac{-5}{-4} \]
Simplifying this fraction:
\[ m = \frac{5}{4} \]
Therefore, the slope of the line that passes through the points \((10, 7)\) and \((6, 2)\) is
\[ \boxed{\frac{5}{4}}. \]