Treat each trip as a point $(d, C)$ on the cost line. What are the two points you can form from the given information?

The rate per mile is the slope of the line between the two points. Use $m = \dfrac{C_2 - C_1}{d_2 - d_1}$ with your two points, then simplify the fraction.

Compute the difference in costs and the difference in miles between the two trips, then divide the cost difference by the miles difference.

In a new expression line, type (29-17)/(9-5) and look at the numeric output that Desmos gives; that value is the taxi company’s constant rate in dollars per mile.

The problem says the cost $C$ is a linear function of the miles $d$, with a fixed booking fee and a constant rate per mile. This can be written in the form

where $m$ is the rate in dollars per mile (what we want) and $b$ is the fixed booking fee.

Each trip gives a pair $(d, C)$:

• A 5-mile trip costs $17, so one point is $(5, 17)$.
• A 9-mile trip costs $29, so another point is $(9, 29)$.

These are two points on the line $C = md + b$.

The rate per mile is the slope $m$ of the line. Use the slope formula with the two points $(5, 17)$ and $(9, 29)$:

This is "change in cost" divided by "change in miles." Do not simplify fully yet.

First compute the numerator and denominator:

• $29 - 17 = 12$
• $9 - 5 = 4$

So

This means the taxi company charges $3$ dollars per mile, so the correct answer is $3$.