A fixed fee plus a constant price per mile gives a linear model. Use two trips to find the price per mile: divide the change in cost by the change in miles. Then start from a known trip and use Desmos to evaluate the cost for the requested mileage. Don’t mistake a known trip’s total cost for the booking fee.
Hints
- Hint 1
Both trip prices include the same booking fee, so subtracting the prices removes it. A rate tells you how much the cost changes for each additional mile. What cost change and mileage change do the two trips show?
- Hint 2
Once you know the price per mile, start from the 3-mile trip. To reach 5 miles, pay for only the miles beyond those first 3, not for all 5 miles again.
Step-by-step
Find the rate, then build from a known trip
Step 1Pair each mileage with its cost
Let mean the total cost, in dollars, of an -mile trip. The two trips give mileage-cost pairs: and . The is the whole 3-mile charge, not the booking fee alone.
- Step 2
Find the price per mile
A rate is the cost added for each extra mile. The fixed booking fee is in both totals, so subtracting the totals removes it. Divide the cost change by the mileage change: . Type in Desmos. It shows , so each extra mile costs $3.
- Step 3
Build the cost rule from 3 miles
The $11 already includes the booking fee. Starting there, an -mile trip adds miles at $3 each: . Type this linear model below the rate calculation in Desmos.
- Step 4
Find the 5-mile total
Type on the next Desmos line. It shows , the total cost of the 5-mile trip, including the booking fee. Choice B.