Let K {\displaystyle {}K} be a field and let W {\displaystyle {}W} be a K {\displaystyle {}K} -vector space. Prove that given two vectors u , v ∈ W {\displaystyle {}u,v\in W} there exists exactly one affine-linear map
sucht that α ( 0 ) = u {\displaystyle {}\alpha (0)=u} and α ( 1 ) = v {\displaystyle {}\alpha (1)=v} .