We investigate the relationship between the continuum enhancement and the hard X-ray (HXR) emission of a white-light flare on 2002 September 29. By reconstructing the RHESSI HXR images in the impulsive phase, we find two bright conjugate footpoints (FPs) on the two sides of the magnetic neutral line. Using the thick-target model and assuming a low-energy cutoff of 20 keV, the energy fluxes of non-thermal electron beams bombarding FPs A and B are estimated to be 1.0 10^10 and 0.8 10^10 ergs/cm^2/s, respectively. However, the continuum enhancement at the two FPs is not simply proportional to the electron beam flux. The continuum emission at FP B is relatively strong with a maximum enhancement of about 8% and correlates temporally well with the HXR profile; however, that at FP A is less significant with an enhancement of only about 4-5%, regardless of the relatively strong beam flux. By carefully inspecting the Halpha line profiles, we ascribe such a contrast to different atmospheric conditions at the two FPs. The Halpha line profile at FP B exhibits a relatively weak amplitude with a pronounced central reversal, while the profile at FP A is fairly strong without a visible central reversal. This indicates that in the early impulsive phase of the flare, the local atmosphere at FP A has been appreciably heated and the coronal pressure is high enough to prevent most high-energy electrons from penetrating into the deeper atmosphere; while at FP B, the atmosphere has not been fully heated, the electron beam can effectively heat the chromosphere and produce the observed continuum enhancement via the radiative backwarming effect.