First, make sure there is a foundation under the slab. Older construction may not have had a foundation, and adding a heavy wall could cause that end to break and sink.
Prep for new wall if slab has a foundation. Drill holes in the slab at the center of the proposed wall. Epoxy rebar in the holes. Build a small form(2x4 with rebar) for a low footer on the slab, pour concrete in the form and add block when set. The rebar will hold the new slab.