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We investigate the observed relationship between black hole mass (M(sub BH)), bolometric luminosity (L(sub bol)) and Eddington ratio (lambda(sub Edd)) with optical emission-line ratios ([N II] lambda6583/Halpha, [S II]lambda-lamda6716, 6731/Halpha, [O I] lamda6300/Halpha, [O III] lamda5007/Hbeta, [Ne III] lamda3869/Hbeta and He II lamda4686/Hbeta) of hard X-ray-selected active galactic nuclei (AGN) from the BAT AGN Spectroscopic Survey. We show that the [N II] lamda6583/Halpha ratio exhibits a significant correlation with lamda(sub Edd) (R(sub Pear) = -0.44, p-value 3 x 10(exp. -13) sigma = 0.28 dex), and the correlation is not solely driven by M(sub BH) or L(sub bol). The observed correlation between [N II] lamda6583/Halpha ratio and M(sub BH) is stronger than the correlation with L(sub bol), but both are weaker than the lamda(sub Edd) 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] lamda6583/Halpha is a useful indicator of Eddington ratio with 0.6 dex of rms scatter, and that it can be used to measure lambda(sub Edd) and thus M(sub BH) from the measured L(sub bol), 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.