AlgebraHardLinear function from two data points in context
Algebra practice question
A courier charges a flat fee plus a rate per kilometre. A 2-kilometre delivery costs $50 and an 8-kilometre delivery costs $74. Which function gives the cost C, in dollars, of a d-kilometre delivery?
- A. C(d) = 4d + 42Correct
- B. C(d) = 25d
- C. C(d) = 4d + 50
- D. C(d) = 12d + 26
Answer: A. C(d) = 4d + 42
Rate: (74 − 50)/(8 − 2) = $4 per km. Fee: 50 − 4 × 2 = $42.
Why the other answers are wrong
- B. C(d) = 25d
- 25d fits the 2-km delivery but gives 200 for 8 km.
- C. C(d) = 4d + 50
- 4d + 50 uses the 2-km cost as the fee; check d = 2: 58 ≠ 50.
- D. C(d) = 12d + 26
- 12d + 26 gives 50 at d = 2 but 122 at d = 8.
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