Vector space/Affine-linear mapping/Example

If we consider vector spaces $V$ and $W$ over a field $K$ as affine spaces, then the affine mappings from $V$ to $W$ have the form

$\psi :V⟶W,v⟼\phi (v)+w,$

where $\phi :V\to W$ is a linear mapping, and $w\in W$ is a fixed vector. In particular, an affine mapping from $K$ to $K$ has the form

$\psi :K⟶K,x⟼ax+b,$

where $a,b\in K$.