To find the slope of line \( e \) that passes through the points \((6, 1)\) and \((1, 9)\), we can use the formula for the slope \( m \) of a line given two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, let's assign \((x_1, y_1) = (6, 1)\) and \((x_2, y_2) = (1, 9)\). Plugging in these values:
\[ m = \frac{9 - 1}{1 - 6} \] \[ m = \frac{8}{-5} \] \[ m = -\frac{8}{5} \]
Since line \( f \) is parallel to line \( e \), it will have the same slope. Therefore, the slope of line \( f \) is:
\[ \boxed{-\frac{8}{5}} \]
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