The National Security Council was created by the National Security Act of 1947 and started functioning in September 1947.
Line agency is when the Congress and the president set goals and to accomplish the agencies help them. Staff agency is when the council offers advice and assistance to the chief executive and other administrators.
An example of the use of the NSC as a line agency is the fight against terror after the attacks of September 11, 2001, when the agency had the authorization to kill individuals who were suspected terrorists.
An example of the use of the NSC as a staff agency is when they advice the president and help him manage international crisis, such as declarations of war.