The correct answer is B) minimum freeboard. The primary purpose of a load line is to establish the minimum freeboard required for a vessel, which is the distance between the waterline and the main deck. This minimum freeboard is determined based on factors such as the vessel's size, type, and intended service, and is regulated by international conventions like the International Convention on Load Lines. Establishing the minimum freeboard ensures the vessel has adequate stability and reserve buoyancy to safely operate in various sea conditions. The other options are incorrect because they are not the primary purpose of a load line. GM (option A) refers to metacentric height, which is a measure of a vessel's transverse stability, but is not directly established by the load line. Transverse stability (option C) is a related but distinct concept from the load line. Fresh water allowances (option D) are a secondary consideration in load line regulations, but not the primary purpose.