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
-4
-1/4
1/4
4
Answers
GPT-4o mini
To find the rate of change (or slope) of a linear function given two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the formula for the slope \(m\):
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Given the points \((-4, 7)\) and \((-1, -5)\):
- Let \((x_1, y_1) = (-4, 7)\)
- Let \((x_2, y_2) = (-1, -5)\)
Now we can substitute these values into the slope formula:
\[
m = \frac{-5 - 7}{-1 - (-4)} = \frac{-5 - 7}{-1 + 4} = \frac{-12}{3} = -4
\]
Therefore, the rate of change for the linear function is \(\boxed{-4}\).
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Given the points \((-4, 7)\) and \((-1, -5)\):
- Let \((x_1, y_1) = (-4, 7)\)
- Let \((x_2, y_2) = (-1, -5)\)
Now we can substitute these values into the slope formula:
\[
m = \frac{-5 - 7}{-1 - (-4)} = \frac{-5 - 7}{-1 + 4} = \frac{-12}{3} = -4
\]
Therefore, the rate of change for the linear function is \(\boxed{-4}\).