In a linear cost model, the starting value is the cost when the input is zero. The number multiplying the input is the rate per unit. Read the constant term, then check what it means when no units have been used. Don't confuse the per-mile rate with the fee charged before travel.
Hints
- Hint 1
In a linear model, the amount multiplied by miles changes as the distance changes. Which number is not multiplied by miles? That number stays in the total even when the ride covers no distance.
- Hint 2
The starting value means the total when the input is zero. Here the input counts miles, so think about a ride at zero miles. What happens to the part of the cost that depends on miles?
Step-by-step
Read the starting cost
Step 1Separate the rate from the fixed amount
No Desmos needed. The fixed term can be read directly from the model.
In , multiplies the miles traveled, so it's the per-mile rate, measured in dollars per mile. The term doesn't depend on the number of miles.
- Step 2
Check the cost at zero miles
The starting value is the total when the input is zero. Before any miles are traveled, , so the miles-based charge disappears:
That leaves dollars in the total cost.
- Step 3
Interpret the fixed cost
So is the initial fee, in dollars, before any miles are traveled. In a linear cost model, the constant is the cost at zero units; the multiplier is the cost per unit. Choice C.