To find the slope \( m \) of a line that passes through two points \((x_1, y_1)\) and \((x_2, y_2)\), we can use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Given the points \((8, 1)\) and \((1, 9)\):
- \( (x_1, y_1) = (8, 1) \)
- \( (x_2, y_2) = (1, 9) \)
Now we can substitute these values into the slope formula:
\[ m = \frac{9 - 1}{1 - 8} \]
Calculating the numerator and denominator:
\[ m = \frac{8}{1 - 8} = \frac{8}{-7} \]
Thus,
\[ m = -\frac{8}{7} \]
The slope of the line that passes through the points (8, 1) and (1, 9) is:
\[ \boxed{-\frac{8}{7}} \]