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.
a. (-1,10) and (0,9)
the rate of change between these two points is - 1
b. (0, ) and (1, )

Explanation:

Step1: Recall slope formula

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

Step2: Identify points for part b

From the graph, when $x = 0$, $y=9$ and when $x = 1$, $y = 6$. So the two - points are $(0,9)$ and $(1,6)$.

Step3: Calculate the rate of change

Substitute $x_1 = 0,y_1=9,x_2 = 1,y_2 = 6$ into the slope formula: $m=\frac{6 - 9}{1-0}=\frac{- 3}{1}=-3$.

Answer:

For part b, the rate of change between the points $(0,9)$ and $(1,6)$ is $-3$.