  We prove that the Moyal product is covariant under linear affine spacetime
transformations. From the covariance law, by introducing an $(x,\Theta)$-space
where the spacetime coordinates and the noncommutativity matrix components are
on the same footing, we obtain a noncommutative representation of the affine
algebra, its generators being differential operators in $(x,\Theta)$-space. As
a particular case, the Weyl Lie algebra is studied and known results for Weyl
invariant noncommutative field theories are rederived in a nutshell. We also
show that this covariance cannot be extended to spacetime transformations
generated by differential operators whose coefficients are polynomials of order
larger than one. We compare our approach with the twist-deformed enveloping
algebra description of spacetime transformations.
