To find the slope of the line that passes through the points \((x_1, y_1) = (5, 1)\) and \((x_2, y_2) = (9, 10)\), you can use the formula for the slope \( m \):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the values of the points into the formula:
\[ m = \frac{10 - 1}{9 - 5} \]
Calculating the differences:
\[ m = \frac{9}{4} \]
Thus, the slope of the line that passes through the points (5, 1) and (9, 10) is
\[ \frac{9}{4} \]