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We investigate the observed relationship between black hole mass (MBH), bolometric luminosity (Lbol) and Eddington ratio (λEdd) with optical emission-line ratios ([N II] λ6583/Ha, [S II] λλ6716, 6731/Hα, [OI] λ6300/Hα, [OIII] λ5007/Hβ, [Ne III] λ3869/Hβ and He II λ4686/Hβ) of hard X-ray-selected active galactic nuclei (AGN) from the BAT AGN Spectroscopic Survey. We show that the [N II] λ6583/Hα ratio exhibits a significant correlation with λEdd (RPear = -0.44, p-value = 3 × 10-13, σ = 0.28 dex), and the correlation is not solely driven by MBH or Lbol. The observed correlation between [N II] λ6583/Hα ratio and MBH is stronger than the correlation with Lbol, but both are weaker than the λEdd correlation. This implies that the large-scale narrow lines of AGN host galaxies carry information about the accretion state of the AGN central engine. We propose that [N II] λ6583/Hα is a useful indicator of Eddington ratio with 0.6 dex of rms scatter, and that it can be used to measure λEdd and thus MBH from the measured Lbol, even for high-redshift obscured AGN.We briefly discuss possible physical mechanisms behind this correlation, such as the mass-metallicity relation, X-ray heating, and radiatively driven outflows. [ABSTRACT FROM AUTHOR]