A linear model fits a fixed fee plus the same charge for each unit: total = (charge per unit)(number of units) + fee. Only the per-unit charge gets multiplied by the number of units. The fee stays even when the input is , so checking the zero-input price can catch a swapped rate and fee.
Hints
- Hint 1
A unit rate tells you the charge for one mile. To find the charge for miles, multiply dollars per mile by miles. Which given amount is the per-mile charge?
- Hint 2
The intercept is the total price when . At zero miles, there's no distance charge, but the fixed fee remains. Where does that fee go in the equation?
Step-by-step
Build the price from the rate and fee
Step 1Find the distance charge
No Desmos needed. The rate and fee are given directly.
The $1.50 per mile is a unit rate: the service charges $1.50 for each mile. Multiply it by miles, so the distance charge is dollars.
- Step 2
Identify the price at zero miles
A fixed fee is paid once, regardless of distance. At , there's no distance charge, but the $3 fee remains. So , meaning the price at zero miles is $3. That's the intercept; don't multiply it by .
- Step 3
Write the total-price equation
Add the one-time fee to the distance charge:
This gives the total price, in dollars, for a delivery of miles. Choice B.