The rate law for an E2 reaction between an alkyl halide $\mathrm{RX}$ and a strong base $\mathrm{B}{}^{-}$ is:

E2 is a single concerted step in which the base and the substrate both take part in the transition state. Hence the rate is first order in $\mathrm{RX}$ and first order in base, $\text{rate}=k[\mathrm{RX}][\mathrm{B}{}^{-}]$ (second order overall). First order in $\mathrm{RX}$ alone is the E1 law.