To find the slope of the line that passes through the points (1, 1) and (10, 2), we can use the formula for the slope \( m \), which is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, we can assign:
- \( (x_1, y_1) = (1, 1) \)
- \( (x_2, y_2) = (10, 2) \)
Now, we can substitute the values into the slope formula:
\[ m = \frac{2 - 1}{10 - 1} \]
Calculating the difference in the y-coordinates:
\[ 2 - 1 = 1 \]
Calculating the difference in the x-coordinates:
\[ 10 - 1 = 9 \]
Now substituting these values back into the slope formula:
\[ m = \frac{1}{9} \]
Thus, the slope of the line that passes through the points (1, 1) and (10, 2) is:
\[ \boxed{\frac{1}{9}} \]