As someone who got introduced to linear algebra this past year, I noticed that we're working with a generalization of the function $y(x)=kx$ for larger dimensions. But the theorems I've been taught don't even include the possibility of what would be $y(x)=kx +n$ (notice the $n$) in $\mathbb{R} \rightarrow \mathbb{R}$ functions. Why is such a seemingly limited tool so important for physics?
(Please, correct me if I said something which is not accurate. Thanks!)