Final answer:
The curved line that connects two repeated notes on the same line or space in music notation is called a tie.
Step-by-step explanation:
The tie is a curved line connecting two repeated notes on the same line or space. The alternatives slur, fermata, and staccato represent different musical notations. A slur also has a curved line but connects notes of different pitch, indicating they should be played legato, or smoothly connected. A fermata indicates that a note should be held longer than its notated value. Staccato means the notes are played shortly and detached.
The tie is written as a curved line above or below the note heads.
For example, if you have two quarter notes on the same line and they are tied together, you would play the first note and hold it for the duration of both notes combined.