This term K-Line was first introduced in 1980 in an essay by Marvin Minsky, entitled K-Lines. In this essay, "K-line" is short for Knowledge-line, a term taken from Artificial Intelligence (AI) or computer science that represents a hypothesized "mental agent" (knowledge that is already present) that comes into play to help a person to formulate a new idea, or solve a problem. This K-line can be likened to a sort of hook that attaches itself to whatever other "mental agents" or existing pieces of knowledge, that are activated by new ideas or problems.
A practical example of this is a teacher assigning an essay or research paper where the student is asked to express their own ideas based on the information presented in class and/or personal research. In this case factual knowledge is combined with original thinking to formulate new ideas.