Question

Find the average rate of change for the given function from x = 0 to x = 4.

Answer 1

Negative one half

One half

−4

4
these are the choices

Answer 2

The rate of change of a graph is the slope of the line. Since the graph is linear, the average rate of change is the same as the actual rate of change.

Answer 3

Just pick any two points. As @walking_stick mentioned, you have a line, so the rate of change is the same for any two points you pick on the line. Obviously, choose 2 points that are easy to read off the graph, such as the x-intercept and y-intercept.

Then you apply the formula:
\[\text{rate of change}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \] where you have 2 coordinates \((x_1, y_1)\) and \((x_2, y_2)\).

The x-intercept is \((4, 0)\) and the y-intercept is \((0,2)\). Can you apply the formula to find the rate of change?

Answer 4

thanks