Question

What is the slope of the line that passes through the points left parenthesis, minus, 5, comma, 6, right parenthesis(−5,6) and left parenthesis, minus, 9, comma, minus, 6, right parenthesis(−9,−6)? Write your answer in simplest form.

Answer 1

To find the slope of the line that passes through the points \((-5, 6)\) and \((-9, -6)\), we can use the formula for the slope \(m\), which is given by:

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

Here, \((x_1, y_1) = (-5, 6)\) and \((x_2, y_2) = (-9, -6)\). Plugging in these values, we get:

\[
m = \frac{-6 - 6}{-9 - (-5)}
\]

Calculating the numerator:

\[
-6 - 6 = -12
\]

Now calculating the denominator:

\[
-9 - (-5) = -9 + 5 = -4
\]

Now substituting back into the slope formula:

\[
m = \frac{-12}{-4} = 3
\]

Thus, the slope of the line that passes through the points \((-5, 6)\) and \((-9, -6)\) is \(\boxed{3}\).