Question

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

Answer 1

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

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