The correct answer is A) across-the-line starters. Across-the-line starters are the most common type of starter used to connect polyphase induction motors to full line voltage at the instant of start-up. This is because across-the-line starters provide a direct connection between the motor and the power source, allowing the motor to start with the full line voltage applied. This type of starter is simple, inexpensive, and suitable for motors that can handle the high starting current required to overcome the initial inertia of the load. The other options (B, C, and D) are less commonly used for this application, as they involve some form of voltage reduction or current limitation during the starting process, which is not necessary for polyphase induction motors that can handle the full line voltage at start-up.