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AlgebraEasy–MediumInterpreting slope in context

Algebra practice question

A phone plan charges a fixed monthly fee plus a charge for each minute of calls. The total monthly cost, in dollars, is given by C(m) = 45 + 0.12m, where m is the number of minutes of calls made that month.

What does 0.12 represent in this model?

  1. A. The cost, in dollars, of each additional minute of calls.Correct
  2. B. The fixed monthly fee, in dollars.
  3. C. The total cost, in dollars, of one month of service.
  4. D. The number of minutes included before extra charges apply.

Answer: A. The cost, in dollars, of each additional minute of calls.

0.12 multiplies m, the number of minutes, so it is the rate: the amount the total cost rises for each additional minute. The 45 that stands alone is the part you pay regardless of usage.

Why the other answers are wrong

B. The fixed monthly fee, in dollars.
The fixed fee is 45 — the term with no m attached. 0.12 is tied to m, so it changes with usage.
C. The total cost, in dollars, of one month of service.
The total cost is the whole expression, 45 + 0.12m, and depends on how many minutes you use. 0.12 is only the per-minute rate.
D. The number of minutes included before extra charges apply.
Nothing in this model gives free minutes; the charge of 0.12 applies from the first minute. 0.12 is a cost in dollars, not a count of minutes.

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