We have studied hypercharge exchange in two pairs of line-reversed reactions at 7 GeV/ c incident beam momentum in a triggered bubble chamber experiment at the SLAC Hybrid Facility. The experiment was carried out with the particular object of testing the predictions of exchange degeneracy using the same apparatus. We present differential and total cross sections for the reactions π +p→ K+Σ +, K-p→π -Σ +and π +p→ K+Y∗+ (1385), K-p→π -Y∗+ (1385) from a π+ exposure of sensitivity 150 events/μb and a K - exposure of 100 events/μb. In each case we have measured the polarization of the final-state hyperon for | t|<1.0 (GeV/ c) 2 by direct observation of its decay in the bubble chamber. We present results from an amplitude analysis of the Y ∗ (1385) reactions and find agreement with the predictions of the additive quark model. The Σ+ polarization data are consistent with weak exchange degeneracy but the predicted equality of the differential cross section is not observed.