Once you have an expression for 3 times $x$, think about what “12 dollars more than” does to that expression. Does it tell you to add 12 or subtract 12?

You now have an expression that represents the total monthly cost based on $x$. How do you write the equation that sets $y$ equal to this expression?

Pick a simple test value for the number of classes, for example $x = 2$. From the description, calculate the cost: first find 3 times 2, then add 12. Keep that resulting cost in mind as the “correct” value for $y$ when $x = 2$.

In Desmos, type each option as a separate line: y = 12x + 3, y = 3x - 12, y = x/3 + 12, and y = 3x + 12. Then, for each equation, open its table (tap the gear icon, then “Table”) and look at the $y$-value when $x = 2$.

Compare the $y$-values from each table at $x = 2$ to the cost you found directly from the wording. The equation whose $y$-value matches that cost is the one that correctly models the relationship.

The problem defines:

• $x$ = number of fitness classes taken in a month.
• $y$ = total monthly cost in dollars.

We need an equation that shows how $y$ depends on $x$.

“3 times the number of fitness classes $x$” means you multiply $x$ by 3. As an algebraic expression, this is:

• $3x$ = three times the number of classes.

“12 dollars more than” means you add 12 to the previous amount.

• Start with $3x$ (three times the number of classes).
• “12 dollars more than $3x$” becomes $3x + 12$.

So the total cost $y$ is given by the expression $3x + 12$.

Because $y$ is the total monthly cost, and it equals “12 dollars more than 3 times $x$,” we write:

This matches answer choice D) $y = 3x + 12$.