1. The problem asks for the equation that represents the total cost $y$ of renting movies over time $x$ months. 2. The service charges a one-time sign-up fee of 10 and then 12 per month. 3. The total cost formula is: $$y = \text{sign-up fee} + (\text{monthly cost} \times \text{number of months})$$ 4. Substitute the values: $$y = 10 + 12x$$ 5. This matches the equation $y = 12x + 10$. 6. The other options either subtract or have incorrect coefficients. 7. Therefore, the correct equation is $y = 12x + 10$.