Recent ROSAT studies of narrow-line Seyfert 1 galaxies revealed these
objects (with FWHM H beta less than or equal to 2000 km s(-1)) general
ly show steeper soft X-ray spectra than broad Line Seyfert 1's and tha
t there are no AGN with broad lines and steep X-ray spectra. We derive
a simple theoretical model which explains this observed correlation b
etween the line width and the spectral index for Seyfert 1 galaxies. A
ssuming the line width is due to gravitational velocity dispersion, it
is determined by the radius of the broad line region. Sources with st
eep X-ray spectra (for a given luminosity) have a stronger ionizing po
wer than flat-spectrum sources with comparable luminosity, which impli
es that the BLR is formed at relatively larger distances from the cent
ral source, and hence has a smaller velocity dispersion and a smaller
observed FWHM. We test the model over a hetrogeneous (normal and narro
w-line) sample of some 50 AGN finding a good agreement with the data.