Question

what is the slope of the line that passes through the points left parenthesis, 3, comma, 8, right parenthesis(3,8) and left parenthesis, minus, 2, comma, 13, right parenthesis(−2,13)? Write your answer in simplest form.

Answer 1

To find the slope of the line that passes through the points \((3, 8)\) and \((-2, 13)\), we use the formula for the slope \(m\) given two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

Here, we can assign:
- \((x_1, y_1) = (3, 8)\)
- \((x_2, y_2) = (-2, 13)\)

Now, substitute the values into the formula:

\[
m = \frac{13 - 8}{-2 - 3}
\]

Calculating the numerator and the denominator:

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

Simplifying this gives:

\[
m = -1
\]

Therefore, the slope of the line that passes through the points \((3, 8)\) and \((-2, 13)\) is \(\boxed{-1}\).