Final answer:
The correct motion when seeking judgment without a trial due to no disputed material facts is a Motion for Summary Judgment. It enables a court to rule in favor of a party when evidence shows there is no need for a jury trial.
Step-by-step explanation:
The appropriate motion to file when a party seeks for the court to enter judgment in the requesting party's favor without going through a trial, due to there being no genuine issues of material fact, is the Motion for Summary Judgment. This motion requests the court to rule that the other party cannot possibly win at trial based on the evidence at hand, thereby obviating the need for a jury trial. A summary judgment is thus entered by the court when substantive evidence indicates that there are no factual disputes requiring a trial for their resolution, and one party is entitled to win as a matter of law.