Question

What is the slope of the line that passes through the points left parenthesis, minus, 7, comma, minus, 2, right parenthesis(−7,−2) and left parenthesis, minus, 15, comma, minus, 14, right parenthesis(−15,−14)? Write your answer in simplest form.

Answer 1

To find the slope of the line that passes through the two points \((-7, -2)\) and \((-15, -14)\), we can use the formula for the slope \(m\):

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

Here, we can assign:

- \((x_1, y_1) = (-7, -2)\)
- \((x_2, y_2) = (-15, -14)\)

Now we substitute the values into the slope formula:

\[
m = \frac{-14 - (-2)}{-15 - (-7)}
\]

This simplifies to:

\[
m = \frac{-14 + 2}{-15 + 7}
\]
\[
m = \frac{-12}{-8}
\]

Now we can simplify \(\frac{-12}{-8}\):

\[
m = \frac{12}{8} = \frac{3}{2}
\]

Therefore, the slope of the line that passes through the points \((-7, -2)\) and \((-15, -14)\) is

\[
\boxed{\frac{3}{2}}.
\]