Question

X: 2.6, 3.2
Y: -6, 3

Determine the rate of change of the linear function given as a table of values.

m=−15

m=−5

m=15

m=0.067

Answer 1

Since the rate of change (m) is equal to the slope of the linear function, we can determine the rate of change for each scenario by comparing the change in y-values to the change in x-values.

1. For m = -15:
Change in y: 3 - (-6) = 9
Change in x: 3.2 - 2.6 = 0.6
m = change in y / change in x = 9 / 0.6 = 15

2. For m = -5:
Change in y: 3 - (-6) = 9
Change in x: 3.2 - 2.6 = 0.6
m = change in y / change in x = 9 / 0.6 = 15

3. For m = 15:
Change in y: 3 - (-6) = 9
Change in x: 3.2 - 2.6 = 0.6
m = change in y / change in x = 9 / 0.6 = 15

4. For m = 0.067:
Change in y: 3 - (-6) = 9
Change in x: 3.2 - 2.6 = 0.6
m = change in y / change in x = 9 / 0.6 = 15

Therefore, the rate of change remains constant at 15 for all scenarios.