1. The problem is to identify which gym membership corresponds to the linear function $y=15x$, where $y$ is the total cost and $x$ is the number of months. 2. The formula $y=15x$ means the cost increases by 15 dollars each month. 3. From the graph, the line passes through $(0,0)$ and $(10,250)$, which suggests a rate of $\frac{250-0}{10-0}=25$ dollars per month. 4. Since the function given is $y=15x$, the cost per month is 15 dollars, not 25. 5. Therefore, the membership that costs 15 dollars per month is Taylor's gym membership. 6. The correct choice is C: Taylor's gym membership at a cost of 15 dollars per month.