Flying the airplane on a constant heading and at a constant altitude is termed:

The term that best describes flying the airplane on a constant heading and at a constant altitude is "Straight-and-level." This phrase specifically refers to maintaining a straight course while flying level, meaning the aircraft is neither climbing nor descending, and its trajectory remains linear.

In practice, straight-and-level flight is fundamental to various aviation maneuvers, as it establishes a baseline from which pilots can safely perform other actions, such as turns or altitude changes. It indicates that the pilot has achieved a state of equilibrium in the forces acting on the aircraft: thrust is equal to drag, and lift is equal to weight.

Other phrases, such as "Level flight," generally imply maintaining altitude but don't explicitly indicate that the aircraft's heading remains constant. "Stable flight" could refer to the aircraft's ability to maintain its flight path with minimal pilot input but lacks the precise definition of the aircraft’s heading. "Controlled flight" may imply that the pilot is actively managing the aircraft's various controls but does not necessarily define the specific scenario of maintaining both heading and altitude constant.