For each function, look at the coefficient (number in front) of $m$. That number should match the cost for each mile.

Try to write a general expression like $T(m) = \text{(rate per mile)}\cdot m + \text{(starting fee)}$, then see which option has the same structure with the correct numbers.

In Desmos, use $x$ to represent miles $m$. Enter each option as a separate function, for example: $y_1=2x-3.50$, $y_2=3.50x+2$, $y_3=2x+3.50$, and $y_4=5.50x$.

For each function, open a table and look at the value when $x=0$. The correct model will have a $y$-value of $3.50 at $x=0$, since that is the flat fee when no miles are traveled.

In each table, look at how $y$ changes when $x$ increases from $1$ to $2$ to $3$, and so on. The correct graph will increase by exactly $2$ dollars for every additional mile, matching the problem description.

The problem describes two separate parts of the taxi cost:

• A flat fee of $3.50: this is what you pay even if you travel $0$ miles.
• $2.00 for each mile traveled: this is the amount added for every mile, so it is the rate per mile.

A linear cost function with a starting fee and a rate per mile has the form

• $T(m) = \text{(rate per mile)} \cdot m + \text{(flat fee)}$

From the problem:

• The rate per mile is $2, so the term with $m$ should be $2m$.
• The flat fee is $3.50, so you should add 3.50 at the end.

Using the pieces from Step 2:

• Rate part: $2m$
• Flat-fee part: $+3.50$

So the total cost function is

Among the answer choices, this corresponds to choice C.