A fixed fee plus a constant charge per mile makes the total cost a linear function: each extra mile adds the same amount. With two trip prices, pair each distance with its cost and find the slope, or change in dollars divided by the matching change in miles. Desmos can evaluate that fraction. Dividing one trip’s total price by its distance wrongly includes the booking fee.
Hints
- Hint 1
An ordered pair puts miles first and total cost second. Keep each distance with its own cost. What pair does each trip give you?
- Hint 2
The slope is the change in cost for one extra mile. Subtract the two costs and divide by the change in miles; dividing one whole fare by its distance also includes the booking fee.
Step-by-step
Find the cost change per mile
Step 1Pair each distance with its cost
In an ordered pair , distance comes first and total cost comes second. So the trips give and . Keep each cost paired with its distance when you compare them.
- Step 2
Divide the cost change by the mileage change
The slope is the dollar change for one additional mile, so divide the cost change by the mileage change:
The booking fee is in both fares, so subtracting removes it. Type into Desmos. It displays , so the taxi company charges $3 per mile. Grid in 3.