Look at how much the total cost $C$ increases when the membership months $m$ increase from 2 to 5. What operation should you use to find the cost per additional month?

Once you know the cost per month, plug it and one of the table points into $C = (\text{monthly fee})m + (\text{sign-up fee})$ to solve for the sign-up fee. Then see which answer choice has those two numbers as its coefficient and constant term.

For each answer choice, use Desmos to compute the predicted costs at $m=2$ and $m=5$ months. For example, for one option type its expression for $C$ at $m=2$ (like 30*2+50) and at $m=5$ (like 30*5+50) on separate lines and note the results.

Repeat this process for all four answer choices. The correct equation is the one whose outputs match both table values exactly: $C=110$ when $m=2$ and $C=185$ when $m=5$.

The problem describes a one-time sign-up fee plus a constant monthly fee.

This means the total cost $C$ after $m$ months has the form

• $C = (\text{monthly fee})\cdot m + (\text{sign-up fee})$.

So we are looking for an equation like $C = (\text{number})m + (\text{number})$ that matches the table values.

From the table:

• At $m=2$, $C=110$.
• At $m=5$, $C=185$.

The monthly fee is the change in total cost divided by the change in months:

So the cost goes up by $25 for each additional month.

Use one of the table points and the monthly fee you just found to solve for the sign-up fee.

Using the point $(m, C) = (2, 110)$ and monthly fee $25:

• Total cost after 2 months is: sign-up fee $+$ $2$ months of fees.

So:

Compute $25\cdot 2 = 50$, then subtract from both sides:

The sign-up fee is $60.

Now plug the monthly fee and sign-up fee into the linear form $C = (\text{monthly fee})m + (\text{sign-up fee})$:

• Monthly fee: $25
• Sign-up fee: $60

So the equation is

This matches answer choice B) $C = 25m + 60$, which is the correct equation.