Question

Line a passes through points (6, 2) and (2, 5). Line b is parallel to line a. What is the slope of line b?

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

Answer 1

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

\[
\boxed{-\frac{3}{4}}
\]