Question

it is possible to find the average rate of change for an interval between two points of a function by finding the slope between the points. use the graph to find the y - value for each x - value. then find the average rate of change for each interval.
b. (0,8) and (1,5)
the rate of change between these two points is - 3
c. (1, ) and (2, )

Explanation:

Step1: Recall slope formula

The formula for the slope (average rate of change) between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Assume points from part c

Let the first - point be $(x_1,y_1)=(1,y_1)$ and the second - point be $(x_2,y_2)=(2,y_2)$. We need to find $y_1$ and $y_2$ from the graph. Suppose from the graph, when $x = 1$, $y_1=6$ and when $x = 2$, $y_2 = 3$.

Step3: Calculate the slope

Substitute the values into the slope formula: $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{3 - 6}{2 - 1}=\frac{-3}{1}=-3$.

Answer:

-3