To find the slope of line \( q \) that passes through the points \( (2, 1) \) and \( (4, 8) \), we can use the formula for the slope \( m \) of a line given two points \( (x_1, y_1) \) and \( (x_2, y_2) \):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Plugging in the points \( (2, 1) \) as \( (x_1, y_1) \) and \( (4, 8) \) as \( (x_2, y_2) \):
\[ m = \frac{8 - 1}{4 - 2} \]
Calculating the differences:
\[ m = \frac{7}{2} \]
Thus, the slope of line \( q \) is \( \frac{7}{2} \). Since line \( r \) is parallel to line \( q \), it will have the same slope.
Therefore, the slope of line \( r \) is:
\[ \boxed{\frac{7}{2}} \]