We have used the Wide Field and Planetary Camera 2 on board the Hubble Space Telescope to obtain V and I images of seven nearby galaxies. For each, we have measured a distance using the tip of the red giant branch (TRGB) method. By comparing the TRGB distances to published Cepheid distances, we investigate the metallicity dependence of the Cepheid period-luminosity relation. Our sample is supplemented by 10 additional galaxies for which both TRGB and Cepheid distances are available in the literature, thus providing a uniform coverage in Cepheid abundances between 1/20 and 2 (O/H)solar. We find that the difference between Cepheid and TRGB distances decreases monotonically with increasing Cepheid abundance, consistent with a mean metallicity dependence of the Cepheid distance moduli of (delta(m-M))/(delta[O/H]) = -0.24 +- 0.05 mag/dex.

Accepted for publication in the Astrophysical Journal. 56 pages, 16 figures (jpg). Version with embedded figures can be retrieved from http://www.astro.ucla.edu/~shoko/pub.html