Cross sections for the γp→K+Λ reaction were measured at backward angles using linearly polarized photons in the range 1.50 to 2.37 GeV. In addition, the beam asymmetry for this reaction was measured for the first time at backward angles. The Λ was detected at forward angles in the LEPS spectrometer via its decay to pπ- and the K+ was inferred using the technique of missing mass. These measurements, corresponding to kaons at far backward angles in the center-of-mass frame, complement similar CLAS data at other angles. Comparison with theoretical models shows that the reactions in these kinematics provide further opportunities to investigate the reaction mechanisms of hadron dynamics.