Question

Find the slope of the line that passes through (8, 1) and (1, 9).

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

Answer 1

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

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

Given the points \((8, 1)\) and \((1, 9)\):
- \( (x_1, y_1) = (8, 1) \)
- \( (x_2, y_2) = (1, 9) \)

Now we can substitute these values into the slope formula:

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

Calculating the numerator and denominator:

\[
m = \frac{8}{1 - 8} = \frac{8}{-7}
\]

Thus,

\[
m = -\frac{8}{7}
\]

The slope of the line that passes through the points (8, 1) and (1, 9) is:

\[
\boxed{-\frac{8}{7}}
\]