We present results from a quantitative spectroscopic analysis conducted on archival Keck/HIRES high-resolution spectra from the California-Kepler Survey (CKS) sample of transiting planetary host stars identified from the Kepler mission. The spectroscopic analysis was based on a carefully selected set of FeI and FeII lines, resulting in precise values for the stellar parameters of effective temperature (Teff) and surface gravity (logg). Combining the stellar parameters with Gaia DR2 parallaxes and precise distances, we derived both stellar and planetary radii for our sample, with a median internal uncertainty of 2.8% in the stellar radii and 3.7% in the planetary radii. An investigation into the distribution of planetary radii confirmed the bimodal nature of this distribution for the small-radius planets found in previous studies, with peaks at ~1.47+/-0.05 and ~2.72+/-0.10R_{Earth}_ with a gap at ~1.9R_{Earth}_. Previous studies that modeled planetary formation that is dominated by photoevaporation predicted this bimodal radii distribution and the presence of a radius gap, or photoevaporation valley. Our results are in overall agreement with these models, as well as core powered mass-loss models. The high internal precision achieved here in the derived planetary radii clearly reveal the presence of a slope in the photoevaporation valley for the CKS sample, indicating that the position of the radius gap decreases with orbital period; this decrease was fit by a power law of the form R_pl_{propto}P^-0.11^, which is consistent with both photoevaporation and core powered mass-loss models of planet formation, with Earth-like core compositions.