In this paper, a closed-loop optimal line-of-sight guidance law for first-order control systems is derived for stationary targets. The problem is solved for the one-dimensional case using normalized equations to obtain normalized guidance gains and performance curves. Three sets of normalized equations are introduced and discussed using different normalizing factors. The performance of the guidance laws are compared in normalized forms with zero-lag optimal guidance and first-order optimal scheme with steady-state gains using a second-order control system. Normalized miss distance analysis shows that the miss distance of the first-order guidance law is smaller than the two mentioned schemes for small total flight times.