If the elements of your vector space are straight lines, then it would make sense to talk about two straight lines being linearly independent. But in this case you would have to define addition of straight lines – what does it mean to “add” two straight lines?
I’d say that most likely you have misquoted or misunderstood something in your textbook. Can you post more information from where you took your question from?
PS: I think you want to say that two straight lines are “linearly independent” iff one cannot be made to coincide with the other by translation alone; in that case two straight lines are “linearly independent” if and only if they are not parallel or coincident. Note that this sense of linear independence is not the same as linear independence of vectors in a vector space.
Last edited by Nehushtan (2014-02-04 04:32:44)