Question

What is the average rate of change for the sequence shown below?

Answer 1

Answer: second option.

Explanation:

The average rate of change is the slope, and this can be calculated with this formula:

`m=(y_2-y_1)/(x_2-x_1)`

Choose two points. Let's choose the points (1,4) and (3,1).

Now, substitute them into the formula
`m=(y_2-y_1)/(x_2-x_1)`. Then you get:

`m=(1-4)/(3-1)\\\\m=-(3)/(2)`

Rewrite this result as a mixed number. Therefore, the answer is:

`m=-1\ (1)/(2)`

This matches with the second option.

Answer 2

B

Explanation:

The average rate of change can be found using formula

`(y_2-y_1)/(x_2-x_1).`

In your case,

`(x_1,y_1)=(4,-0.5),\\ \\(x_2,y_2)=(1,4).`

Hence,

`(-0.5-4)/(4-1)=(-4.5)/(3)=-1.5=-1(1)/(2).`