Question

What is the slope of the line that passes through the points left parenthesis, 6, comma, minus, 5, right parenthesis(6,−5) and left parenthesis, minus, 6, comma, minus, 5, right parenthesis(−6,−5)? Write your answer in simplest form.

Answer 1

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

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

In this case, we have the points \((6, -5)\) and \((-6, -5)\). We can assign:

- \((x_1, y_1) = (6, -5)\)
- \((x_2, y_2) = (-6, -5)\)

Now, substituting these values into the slope formula:

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

Calculating the values:

\[
m = \frac{-5 + 5}{-6 - 6} = \frac{0}{-12}
\]

Since the numerator is 0, the slope \( m \) becomes:

\[
m = 0
\]

This indicates that the line is horizontal. Therefore, the slope of the line that passes through the points \((6, -5)\) and \((-6, -5)\) is

\[
\boxed{0}
\]