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.

1 answer

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

\[ \boxed{0} \]