A microscope-mounted torsional shearing-flow cell is constructed and microscopic particle imaging velocimetry is employed to directly visualize and map the velocity slip layer in a shearing flow of dilute micellar surfactant solutions of cetyltriammonium bromide/sodium salicylate. It is shown that the thickness of the wall-slip layer is about 100 mum at low shear rates, decreasing to around 50-60 mum at high shear rates. Surprisingly, we find that the wall slip layer emerges only near the upper rotating plate of the flow cell, and not the lower surface. The theological properties of the wormy micellar solutions are also measured by using a stress-controlled rheometer and the results are compared to the visualization results of wall-slip velocity in the shearing-flow cell. The rheometer measurements are consistent with literature reports [Hu et al. (1998a, 1998b)] in that there is a critical shear rate at which the apparent shear viscosity increases drastically. Above the critical point, the shear viscosity reaches a plateau and decreases at a higher shear rate where we observe that the flow becomes unstable. As the gap of parallel plate geometry or the cone angle of cone-plate geometry increases, the critical shear rate decreases, because the wall-slip layer forms in the flow cell even below the shear thickening transition. We extract the wall-slip velocities from the theological data using a Mooney analysis and show, apparently for the first time, that the slip velocity from the Mooney analysis is consistent with that obtained by direct visualization experiments.