Question 457·Medium·Algebra

No Desmos needed. Equal mile gaps have equal fare increases at a constant rate. Compare the distances on either side of the 8-mile ride:

So 8 miles is halfway between the two known distances.

The constant rate means equal mileage gaps give equal fare increases. Find the price change across the whole trip from 5 to 11 miles:

The requested mileage is the midpoint of the known mileages, so its fare is halfway between their prices. Take half the $12 increase:

That’s the extra cost from 5 miles to 8 miles.

Start with the $19 fare for 5 miles. It already includes the flat fee, the charge paid once per ride. Add the extra cost:

An 8-mile ride costs $25. Choice B.

The rate is the price increase per mile. The flat fee is in both fares, so subtracting the fares removes it. Type $m=\frac{31-19}{11-5}$ in Desmos; it shows $m=2$, so the rate is $2 per mile.

The $19 fare already includes the flat fee, so add only the charge for miles beyond 5. Keep the $m$ line and type $c(x)=19+m(x-5)$ in Desmos, where $x$ means miles and $c(x)$ means the cost in dollars.

Type $c(8)$ to put 8 miles into the model. Desmos displays $25$. The 8-mile ride costs $25. Choice B.