Question

your cellular phone contract calls for a flat monthly service charge of $10.95 plus $0.12 per minute for calls within a certain area to which you limit your calls. the table shows some cost data for your use of the phone.
number of minutes | monthly cost (dollars)
100 | 22.95
120 | 25.35
140 | 27.75
160 | 30.15
does the data represent a linear function? why or why not?
a. no, the average rate of change is not constant
c. there is not enough information to determine if this is a linear function.
b. yes, the average rate of change is constant. d. no, this is not a linear function.

Explanation:

To determine if the data is linear, we check the average rate of change (slope) between consecutive points.

For 100 to 120 minutes:
Change in cost = \( 25.35 - 22.95 = 2.4 \)
Change in minutes = \( 120 - 100 = 20 \)
Rate of change = \( \frac{2.4}{20} = 0.12 \) dollars per minute.

For 120 to 140 minutes:
Change in cost = \( 27.75 - 25.35 = 2.4 \)
Change in minutes = \( 140 - 120 = 20 \)
Rate of change = \( \frac{2.4}{20} = 0.12 \) dollars per minute.

For 140 to 160 minutes:
Change in cost = \( 30.15 - 27.75 = 2.4 \)
Change in minutes = \( 160 - 140 = 20 \)
Rate of change = \( \frac{2.4}{20} = 0.12 \) dollars per minute.

Since the rate of change (slope) is constant (\( 0.12 \) dollars per minute) between all consecutive data points, the data represents a linear function.

Answer:

b. Yes, the average rate of change is constant.