Line c passes through points (-41, 72) and (13, 48). Line d is parallel to line c. What is the slope of line d?]

1 answer

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

\[ \boxed{-\frac{4}{9}}. \]