Question

The graph of a linear function contains the points (-4, 7) and (-1, -5). What is the rate of change for this linear function?

-4
-1/4
1/4
4

Answer 1

To find the rate of change (slope) of the linear function that passes through the points (-4, 7) and (-1, -5), we can use the formula for the slope \( m \):

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

Let's assign the points:
- \( (x_1, y_1) = (-4, 7) \)
- \( (x_2, y_2) = (-1, -5) \)

Now, we can plug the coordinates into the slope formula:

\[
m = \frac{-5 - 7}{-1 - (-4)}
\]

Calculating the differences:

\[
m = \frac{-5 - 7}{-1 + 4}
\]
\[
m = \frac{-12}{3}
\]
\[
m = -4
\]

Thus, the rate of change (slope) for the linear function is \(-4\).

The correct answer is \(-4\).