A linear model fits a fixed fee plus a charge that repeats with each unit. To write the total cost, identify what is paid once and what changes with the number of miles. Multiply the per-mile rate by the miles; add the fixed fee once. Swapping those jobs makes the fee grow with distance.
Hints
- Hint 1
The starting value is the cost at zero miles. A fixed fee is paid once, even when the distance changes. Which amount in the story is still charged at zero miles?
- Hint 2
A rate tells you the charge for each mile. Multiply the per-mile amount by to get the part of the cost that changes with distance. How does that combine with the fixed fee?
Step-by-step
Separate the fixed fee from the per-mile charge
Step 1Find the cost before any miles
No Desmos needed. The job is to build an equation from the charges, not solve one.
At miles, there's no mileage charge, but the fixed booking fee still applies. So the starting value, the cost before any miles, is $2.
- Step 2
Write the charge that changes with miles
The $1.50 per mile is a rate: it is charged for every mile traveled. Multiply it by the number of miles:
So is the mileage charge, in dollars.
- Step 3
Add the charges to get the total
Add the one-time fee to the mileage charge, the part that changes with distance:
So this equation gives the total cost in dollars for an -mile ride. Choice D.