Let $(X,d)$ be a real metric linear space,
with translation-invariant metric $d$ and $G$
a linear subspace of $X$. In this paper we use
functionals in the Lipschitz dual of $X$ to
characterize those elements of $G$ which are
best approximations to elements of $X$.
We also give simultaneous characterization of
elements of best approximation and also
consider elements of $\epsilon$-approximation.