16Hit1600
AlgebraHardLinear function from two input-output pairs in context

Algebra practice question

A plumber charges a fixed call-out fee plus an hourly rate. A 2-hour job costs $35 and a 6-hour job costs $95. Which function gives the cost C, in dollars, of a job lasting h hours?

  1. A. C(h) = 15h + 5Correct
  2. B. C(h) = 17.5h
  3. C. C(h) = 15h + 35
  4. D. C(h) = 10h + 15

Answer: A. C(h) = 15h + 5

Rate: (95 − 35)/(6 − 2) = $15 per hour. Fee: 35 − 2(15) = $5.

Why the other answers are wrong

B. C(h) = 17.5h
17.5h fits the 2-hour job but gives 105 for 6 hours.
C. C(h) = 15h + 35
15h + 35 uses the 2-hour cost as the fee; check h = 2: 65 ≠ 35.
D. C(h) = 10h + 15
10h + 15 gives 35 at h = 2 but 75 at h = 6.

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