Setting $y$ to 1, we have $1=\frac{1}{3x+1}$.
Multiplying both sides by $3x+1$, we have $3x+1=1$.
Subtracting 1 from both sides, we have $3x=0$.
Dividing both sides by 3, we have $x=\boxed{0}$.
The answer is: 0
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
What is the value of $x$ when $y = 1$ in the equation $y = \frac{1}{3x+1}$?

### Answer:
