The function f(x)=mx is linear but the function g(x)=mx+b is not linear.
g(x) is affine.
A Real Space R^n has an origin.
An Affine Space A^n does not have an origin.
A piece of graph paper in the package is an A^2 space.
When you circle an intersection to say this point is the origin, you make it an R^2 space.
We cannot calculate the sum of two points in an affine space but we can calculate the difference between two points in an affine space.