A taxi-fare equation is a linear model: it combines a charge that grows with distance and a fixed starting charge. The number multiplying miles is the slope, meaning the extra dollars charged for each mile. The number added at the end is the fare before any miles are driven. Don't confuse a dollars-per-mile rate with a speed or the cost of an entire ride.
Hints
- Hint 1
The slope is how much the output changes when the input goes up by one. Here, fare is the output and miles are the input. Which number is multiplied by the miles?
- Hint 2
Use the units to check your interpretation. A change in dollars for each additional mile is dollars per mile, not miles per hour. The number added without being multiplied by miles is the starting charge.
Step-by-step
Read the rate from the equation
Step 1Identify the mileage rate
No Desmos needed. The equation shows the rate directly. In a linear equation, the number multiplying the miles is the slope, or how much the fare changes for one extra mile. In , that number is .
- Step 2
Give the rate its meaning and units
The fare is in dollars, and is in miles, so the slope is in dollars per mile, not miles per hour. The is added regardless of mileage, so it's the starting charge. The fare increases by $2.50 for each additional mile. Choice B.