Question

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

Answer 1

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

Answer 2

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