Question 667·Medium·Algebra

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A satellite phone company offers a plan whose total monthly cost, in dollars, can be modeled by the function

C(m)=0.75m+25

where $m$ is the number of minutes used in a month.

Which statement is the best interpretation of the slope of the graph of $y=C(m)$ in the $xy$ -plane in this context?

In a linear cost model, the slope is the change in cost for one more unit of the input. When the input counts minutes, read the slope in dollars per minute. You can confirm it in Desmos by comparing the costs at zero and one minute. Don't confuse the fixed monthly fee with the amount charged for each minute.

Hints

Hint 1
A slope compares the change in the output with the change in the input. Here the output is cost and the input is minutes, so what units should the cost change have?
Hint 2
In a linear function, the amount that stays the same when the input changes is the starting value. Compare $C(1)$ with $C(0)$ to find what one extra minute adds.

Step-by-step

Compare the cost for one more minute
Step 1
Identify the slope's units
The input $m$ counts minutes, and the output $C(m)$ is a cost in dollars. A slope tells you the output change for one more unit of input, so its units here are dollars per minute, not dollars per month.
Step 2
Find the cost at zero minutes
To separate the starting cost from the per-minute charge, type $C(m)=0.75m+25$ , then $C(0)$ in Desmos. It shows $25$ . That's the fixed fee paid with zero minutes of usage, so it isn't the slope.
Step 3
Find what one minute adds
Add $C(1)-C(0)$ in Desmos. It shows $0.75$ : the monthly cost rises by $0.75 for one additional minute. The slope is the charge per minute, while the fixed fee is the cost at zero minutes. Choice B.

Question 667·Medium·Algebra

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