Catalyzes the conversion of alpha-linoleate to (9R,10E,12Z,15Z)-9-hydroperoxyoctadeca-10,12,15-trienoate in oxylipin biosynthesis. Also converts alpha-linoleate to (9R,10E,12Z)-9-hydroperoxyoctadeca-10,12-dienoate. (9Z,12Z,15Z)-octadecatrienoate + O2 = (9R,10E,12Z,15Z)-9-hydroperoxyoctadeca-10,12,15-trienoate Optimum pH is 7-10. Lipid metabolism; oxylipin biosynthesis. Belongs to the lipoxygenase family.