Final answer:
The type of authority allowing a supervisor to direct employees without consulting others is line authority, reflecting a direct chain of command within the organizational hierarchy.
Step-by-step explanation:
The type of authority that gives a supervisor the right to direct the work of his or her employees without consulting others is known as line authority. Line authority is derived from the position within the organizational hierarchy and grants a manager control over subordinates. It represents a direct chain of command within the organization and does not require the consent or advice of others to enforce decisions or give instructions. This is in contrast to other types of authority like legal authority, which is based on laws and regulations; charismatic authority, which stems from an individual's personal qualities and appeal; and traditional authority, which is centered around longstanding customs or practices.