To find the slope of line \(d\), which is parallel to line \(c\), we first need to calculate the slope of line \(c\) using the two given points \((-41, 72)\) and \((13, 48)\).
The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the coordinates of the points into the formula where \((x_1, y_1) = (-41, 72)\) and \((x_2, y_2) = (13, 48)\):
\[ m = \frac{48 - 72}{13 - (-41)} \] \[ m = \frac{48 - 72}{13 + 41} \] \[ m = \frac{-24}{54} \]
Now, simplify \(\frac{-24}{54}\):
\[ m = \frac{-4}{9} \]
The slope of line \(c\) is \(-\frac{4}{9}\). Since line \(d\) is parallel to line \(c\), it will have the same slope.
Thus, the slope of line \(d\) is
\[ \boxed{-\frac{4}{9}}. \]