A linear cost model fits a flat fee plus a price per mile: the fee is paid once, while the mileage charge grows with distance. Write total cost as a function of miles, then evaluate it in Desmos at the trip distance. Multiply the per-mile rate by miles, not the flat fee.
Hints
- Hint 1
A flat fee is paid once, no matter how far the taxi goes. Which amount stays unchanged when you write a rule for the cost of miles?
- Hint 2
A rate of $2 per mile means $2 for each mile. Multiply it by the number of miles, then add the flat fee to get the total.
Step-by-step
Build and evaluate a cost rule
Step 1Write the two-part cost rule
Let be the number of miles and be the total cost in dollars. The flat fee is paid once, so stays fixed. The $2 per mile charge becomes , so . Type this rule in Desmos to use it for the trip.
- Step 2
Find the cost for 12 miles
Type below the rule because the trip is 12 miles. Desmos displays . The per-mile rate gets multiplied by miles; the flat fee is added once. The total trip cost is $27. Choice D.