Question

A line passes through the points (-2, 7) and (3, -8).
Part I: Calculate the slope of the line. Show ALL your work.

Answer 1

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

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

Here, we have the points:

- Point 1: \((-2, 7)\) which gives us \(x_1 = -2\) and \(y_1 = 7\)
- Point 2: \((3, -8)\) which gives us \(x_2 = 3\) and \(y_2 = -8\)

Now, substituting these values into the slope formula:

1. Calculate \(y_2 - y_1\):
\[
y_2 - y_1 = -8 - 7 = -15
\]

2. Calculate \(x_2 - x_1\):
\[
x_2 - x_1 = 3 - (-2) = 3 + 2 = 5
\]

Now, substitute these results into the slope formula:

\[
m = \frac{-15}{5}
\]

Simplifying this gives:

\[
m = -3
\]

Thus, the slope of the line is:

\[
\boxed{-3}
\]