Question

Find the slope of the line that passes through (10, 8) and (5, 16).

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

Answer 1

To find the slope of the line that passes through the points \((x_1, y_1) = (10, 8)\) and \((x_2, y_2) = (5, 16)\), we can use the formula for the slope \(m\) between two points:

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

Substituting in the coordinates of the points:

\[
m = \frac{16 - 8}{5 - 10}
\]

Calculating the differences in the numerator and the denominator:

\[
m = \frac{8}{5 - 10} = \frac{8}{-5}
\]

This simplifies to:

\[
m = -\frac{8}{5}
\]

Thus, the slope of the line that passes through the points \((10, 8)\) and \((5, 16)\) is

\(\boxed{-\frac{8}{5}}\).