To find the slope of line \( b \), we first need to determine the slope of line \( a \), which passes through the points \((6, 2)\) and \((2, 5)\).
The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Plugging in our points \((x_1, y_1) = (6, 2)\) and \((x_2, y_2) = (2, 5)\):
\[ m = \frac{5 - 2}{2 - 6} \] \[ m = \frac{3}{-4} \] \[ m = -\frac{3}{4} \]
Since line \( b \) is parallel to line \( a \), it will have the same slope.
Thus, the slope of line \( b \) is
\[ \boxed{-\frac{3}{4}} \]