A linear model fits a total made from a fixed starting amount and a charge that repeats at a constant rate. Look for a flat fee alongside a price "for each" unit. Multiply only the per-unit price by the number of units, then add the fee once. Swapping their jobs makes the fee repeat instead.
Hints
- Hint 1
A rate tells you how much the cost changes for each mile. To find the charge for miles, which given dollar amount must be multiplied by ?
- Hint 2
A starting value is the cost when no miles have been traveled. The flat fee is paid once, even at . Which charge would still be on the bill?
Step-by-step
Match each charge to its job
Step 1Find the charge that grows with miles
No Desmos needed. The fee and per-mile rate already tell you the equation's parts. The per-mile charge is $2.50. A rate is the charge for one mile, so multiplying by miles gives a distance charge of dollars.
- Step 2
Keep the flat fee separate
The flat fee is charged once when the passenger enters. Even at , that charge is $4, so . Don't multiply the $4 by ; it doesn't recur each mile.
- Step 3
Write the total cost
is the total cost, so add the distance charge and the fee:
Multiply the per-unit charge by the number of units; add the one-time fee once. This equation gives the ride's cost in dollars for miles. Choice B.