Question

3.
Find the slope of the line that passes through the pair of points.

(1, 7), (10, 1)

Answer 1

To find the slope \( m \) of the line that passes through the points \((x_1, y_1) = (1, 7)\) and \((x_2, y_2) = (10, 1)\), we can use the formula for the slope:

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

Substituting in the coordinates of the points:

\[
m = \frac{1 - 7}{10 - 1}
\]

Calculating the difference in the y-coordinates:

\[
1 - 7 = -6
\]

And calculating the difference in the x-coordinates:

\[
10 - 1 = 9
\]

Now, substituting these values back into the slope formula:

\[
m = \frac{-6}{9}
\]

This can be simplified:

\[
m = \frac{-2}{3}
\]

So, the slope of the line that passes through the points \((1, 7)\) and \((10, 1)\) is

\[
\boxed{-\frac{2}{3}}.
\]