my linear algebr textbook defines a linear transformation/map as one that satisfies:
i. T(u+v)=T(u) +T(v). ii. T(cu) = cT(u)
However, what is traditionally called a linear function, in non-abstract algebra (or highschool algebra, or whatever it is formally called), namely: f(x) = a + bx is not a linear mapping according to the linear algebra definition, unless a = 0.
Is there an intuitive reason why the first definition is called a linear map, and why you would not call y=1+x a linear map, despite the fact that it defines a straight line on a plane? I could simply take the definitions as given, but it always helps me to have an intuitive understanding of such terminology.