Question

What is the slope of the line that passes through the points left parenthesis, minus, 4, comma, 4, right parenthesis(−4,4) and left parenthesis, minus, 1, comma, 3, right parenthesis(−1,3)? Write your answer in simplest form.

Answer 1

To find the slope of the line that passes through the points \((-4, 4)\) and \((-1, 3)\), we can use the slope formula:

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

where \((x_1, y_1) = (-4, 4)\) and \((x_2, y_2) = (-1, 3)\).

Substituting the values into the formula, we get:

\[
m = \frac{3 - 4}{-1 - (-4)}
\]

Calculating the numerator:

\[
3 - 4 = -1
\]

Calculating the denominator:

\[
-1 - (-4) = -1 + 4 = 3
\]

Now substituting these values back into the slope formula:

\[
m = \frac{-1}{3}
\]

Thus, the slope of the line that passes through the points \((-4, 4)\) and \((-1, 3)\) is:

\[
\boxed{-\frac{1}{3}}
\]