Question

What is the rate of change of the function?

On a coordinate plane, a line with positive slope goes through points (0, negative 4) and (2, 2).
–3
Negative one-third
One-third
3

Answer 1

To find the rate of change of the function represented by the line through the points (0, -4) and (2, 2), we can calculate the slope, which is the rate of change.

The formula for the slope \( m \) of a line given two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

For the points \((0, -4)\) and \((2, 2)\):

- \(x_1 = 0\), \(y_1 = -4\)
- \(x_2 = 2\), \(y_2 = 2\)

Plugging these values into the formula gives:

\[
m = \frac{2 - (-4)}{2 - 0} = \frac{2 + 4}{2} = \frac{6}{2} = 3
\]

Thus, the rate of change of the function is \(3\).

The answer is **3**.