Question

What is the rate of change for the linear relationship modeled in the table?

X Y
-1 10
1 9
3 8
5 7

A) -1/2
B) 0
C) 1/2
D) 2

Answer 1

Take any 2 points and find the slope of the line connecting them:

1 9
3 8
9-8 1
slope m is m = ------- = -------- = -1/2
1-3 -2

Answer 2

Since the data represented by the table are linear, then the average rate of change is given by the slope of the line.
We have then:

`m = (y2-y1) / (x2-x1)`
Substituting values we have:

`m = (9-10) / (1 - (- 1))`
Rewriting we have:

`m = (-1) / (1 + 1) m = -1/2`
Answer:
The average rate of change is given by:
A) -1/2