Final answer:
The primary line element in a police agency is patrol services, constituting the core public-facing duties like routine patrols and responding to emergencies. The correct answer is option A).
Step-by-step explanation:
The primary line element in a police agency is known as patrol services. Patrol services are the most visible and fundamental aspect of a police department's operations. Officers in patrol services are responsible for routine patrols, responding to emergency calls, ensuring public safety, and maintaining law and order within the community. In contrast, staff services typically involve administrative roles, auxiliary services might include specialized technical functions, and investigations pertain to the examination of crimes and gathering evidence.