Question

Find the slope of the line passing through the points (3, 8) and (7, - 7).

Answer 1

To find the slope \( m \) of the line passing through the points \((x_1, y_1)\) and \((x_2, y_2)\), we use the formula:

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

For the points \((3, 8)\) and \((7, -7)\), we have:

- \(x_1 = 3\), \(y_1 = 8\)
- \(x_2 = 7\), \(y_2 = -7\)

Substituting these values into the slope formula gives:

\[
m = \frac{-7 - 8}{7 - 3}
\]

Calculating the numerator:

\[
-7 - 8 = -15
\]

Calculating the denominator:

\[
7 - 3 = 4
\]

Now, substituting these results into the slope formula:

\[
m = \frac{-15}{4}
\]

Thus, the slope of the line passing through the points \((3, 8)\) and \((7, -7)\) is

\[
\boxed{-\frac{15}{4}}.
\]