The correct answer is A) passing a messenger line. Heaving lines are used to pass a lightweight line (the messenger line) from one vessel to another, typically when towing another vessel. The messenger line is then used to pull a heavier tow line or tow bridle across from the towing vessel to the vessel being towed. This allows the tow connection to be established without having to throw or physically pass the heavy tow line directly. The other answer choices do not accurately describe the primary purpose of heaving lines in the towing context.