Question

What is the slope of the line that passes through the points left parenthesis, 2, comma, 8, right parenthesis(2,8) and left parenthesis, minus, 3, comma, 14, right parenthesis(−3,14)? Write your answer in simplest form.

Answer 1

To find the slope of the line that passes through the points \((2, 8)\) and \((-3, 14)\), we can use the formula for the slope \(m\):

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

Here, we can assign:
- \((x_1, y_1) = (2, 8)\)
- \((x_2, y_2) = (-3, 14)\)

Now substituting the values into the slope formula:

\[
m = \frac{14 - 8}{-3 - 2}
\]

Calculating the differences in the numerator and the denominator:

\[
m = \frac{6}{-5}
\]

Thus, the slope of the line is:

\[
m = -\frac{6}{5}
\]

So, the slope of the line that passes through the points \((2, 8)\) and \((-3, 14)\) is \(\boxed{-\frac{6}{5}}\).