Question

Line e passes through points (6, 1) and (1, 9). Line f is parallel to line e. What is the slope of line f?

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answer 1

To find the slope of line \( e \) that passes through the points \((6, 1)\) and \((1, 9)\), we can use the formula for the slope \( m \) of a line given two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Here, let's assign \((x_1, y_1) = (6, 1)\) and \((x_2, y_2) = (1, 9)\). Plugging in these values:

\[
m = \frac{9 - 1}{1 - 6}
\]
\[
m = \frac{8}{-5}
\]
\[
m = -\frac{8}{5}
\]

Since line \( f \) is parallel to line \( e \), it will have the same slope. Therefore, the slope of line \( f \) is:

\[
\boxed{-\frac{8}{5}}
\]