We present an improved measurement of the left-right cross section asymmetry Alr for Z boson production by e+e- collisions. The measurement was performed at a center-of-mass energy of 91.28 GeV with the SLD detector at the SLAC Linear Collider (SLC) during the 1994-95 running period. The luminosity-weighted average polarization of the SLC electron beam during this run was measured to be (77.23 +/- 0.52)%. Using a sample of 93,644 hadronic Z decays, we measure the pole asymmetry Alr0 to be 0.1512 +/- 0.0042(stat.) +/- 0.0011(syst.) which is equivalent to an effective weak mixing angle of 0.23100 +/- 0.00054(stat.) +/- 0.00014(syst.). We also present a preliminary direct measurement of the Z-lepton coupling asymmetries A_e,A_mu, and A_tau extracted from the differential cross section observed in leptonic Z decays. We combine these results with our previous Alr measurement to obtain a combined determination of the weak mixing angle of 0.23061 +/- 0.00047
