A line is classically defined as a connection between two points. I say "classically" because that is the way that classic geometry texts – specifically Euclid’s Thirteen Books of the Elements – defined it in definitions II and III:

Euclid was really defining a straight line. But artists and designers know that lines come in many different configurations: they can be curvy or wavy; they can be jagged and rough; they can demarcate a border between things, thereby separating them. But they can also connect things together. They can imply movement, draw our attention to things, or obscure things. Lines can be angry, sad, mysterious, direct, or implied by the alignment of other elements (a.k.a. implied lines).