We present a study of the variation of the relative abundance of helium to hydrogen in the solar wind as a function of solar wind speed and heliographic latitude over the previous solar cycle. The average values of A_He, the ratio of helium to hydrogen number densities, are calculated in 25 speed intervals over (~27 day) Carrington rotations using Faraday cup observations from the Wind spacecraft between 1995 and 2005. We find that for solar wind speeds between 350 and 415 km s^-1, A_He varies with a clear 6 month periodicity, with a minimum value at the heliographic equatorial plane and a typical gradient of 1% per degree in latitude. Once the gradient is subtracted, we find that A_He is a remarkably linear function of solar wind speed. We identify the implied speed at which A_He is zero as 259 ± 12 km s^-1 and note that this speed corresponds to the minimum solar wind speed observed at 1 AU. The vanishing speed may be related to previous theoretical work in which enhancements of coronal helium lead to stagnation of the escaping proton flux. During solar maximum the A_He dependences on speed and latitude disappear, and we interpret this as evidence of two source regions for slow solar wind in the ecliptic plane, one being the solar minimum streamer belt and the other likely being active regions.