The phrase "constant rate per mile" corresponds to the slope of a line. Use the two points to compute the slope using $\dfrac{\text{change in cost}}{\text{change in miles}}$.

Write an equation in the form $C(m) = rm + b$, where $r$ is the rate per mile you just found. Plug in one of the trips (a point) to solve for $b$, the flat fee.

Once you know the rate per mile and the flat fee, write your linear equation and see which answer choice exactly matches it.

Type each answer choice into Desmos as a separate line: C(m) = 2m + 8, C(m) = 2.5m + 4, C(m) = 3m + 6, and C(m) = 2m + 6. Desmos will graph four straight lines.

In Desmos, add a table with an $m$ column and values $6$ and $14$. For each equation, create an expression like C1(6) and C1(14) (using the function names you chose) or click on the graphs at $m = 6$ and $m = 14$ to see the $y$‑values. Identify which equation gives cost $18 at $m = 6$ and cost $34 at $m = 14$; that is the correct choice.

We are told the total cost for two different trips:

• A 6‑mile trip costs $18.
• A 14‑mile trip costs $34.

We can think of each trip as a point $(m, C)$ on a line, where $m$ is miles and $C$ is cost:

• First trip: $(6, 18)$
• Second trip: $(14, 34)$

These two points lie on the line that represents the cost function $C(m)$.

The taxi charges a constant rate per mile, so the rate per mile is the slope of the line that goes through $(6, 18)$ and $(14, 34)$.

Use the slope formula $m = \dfrac{\Delta y}{\Delta x}$:

So the constant rate per mile is $2$ dollars per mile.

A linear cost function with slope $2$ has the form

where $b$ is the flat fee (the starting cost when $m = 0$).

Use one of the points to solve for $b$. Using $(6, 18)$:

• Plug in $m = 6$ and $C = 18$:

• Simplify $2(6)$:

• Subtract $12$ from both sides:

So the flat fee is $6$ dollars.

Now we know:

• Rate per mile (slope) $= 2$
• Flat fee (y‑intercept) $= 6$

So the cost function is

Looking at the answer choices, this matches choice D) $C(m) = 2m + 6$, which is the correct equation.