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Observations show that star-forming galaxies reside on a tightthree-dimensional plane between mass, gas-phase metallicity and star formationrate (SFR), which can be explained by the interplay between metal-poor gasinflows, SFR and outflows. However, different metals are released on differenttime-scales, which may affect the slope of this relation. Here, we use central,star-forming galaxies with M$_{\rm star}=10^{9.0-10.5}$ M$_{\odot}$ from theEAGLE hydrodynamical simulation to examine three-dimensional relations betweenmass, SFR and chemical enrichment using absolute and relative C, N, O and Feabundances. We show that the scatter is smaller when gas-phase$\alpha$-enhancement is used rather than metallicity. A similar plane alsoexists for stellar $\alpha$-enhancement, implying that present-day specificSFRs are correlated with long time-scale star formation histories. Between$z=0$ and 1, the $\alpha$-enhancement plane is even more insensitive toredshift than the plane using metallicity. However, it evolves at $z>1$ due tolagging iron yields. At fixed mass, galaxies with higher SFRs have starformation histories shifted toward late times, are more $\alpha$-enhanced andthis $\alpha$-enhancement increases with redshift as observed. These findingssuggest that relations between physical properties inferred from observationsmay be affected by systematic variations in $\alpha$-enhancements.

Star-forming galaxies are predicted to lie on a fundamental plane of mass, star formation rate and \alpha-enhancement