Question

What is the slope of the line that passes through the points left parenthesis, minus, 4, comma, 2, right parenthesis(−4,2) and left parenthesis, minus, 5, comma, 0, right parenthesis(−5,0)? Write your answer in simplest form.

Answer 1

To find the slope of the line that passes through the points \((-4, 2)\) and \((-5, 0)\), we can use the formula for the slope \( m \) which is given by:

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

Here, we can assign \( (x_1, y_1) = (-4, 2) \) and \( (x_2, y_2) = (-5, 0) \).

Now, substituting the coordinates into the slope formula:

\[
m = \frac{0 - 2}{-5 - (-4)}
\]

Simplifying the numerator and the denominator:

\[
m = \frac{-2}{-5 + 4} = \frac{-2}{-1}
\]

This simplifies to:

\[
m = 2
\]

Thus, the slope of the line that passes through the points \((-4, 2)\) and \((-5, 0)\) is \(\boxed{2}\).