When it comes to synonyms for the phrase "line cut", there are several options to consider. To begin with, a "line incision" or "cut on a line" would convey a similar meaning. Alternatively, one could use "score" or "crease" to describe a cut along a pre-determined path. Another synonym to consider might be "slot," which is a narrow opening or groove made in a material. Finally, "slit" could be another viable option, as it's a small cut made in something typically to facilitate a function or create a particular look. Ultimately, the choice of synonym depends on the context and intended meaning.