Try Delta. SLC is a hub, LAX is a focus city.

I don't think NW flies SLC-LAX, and since they're so close you will likely have a hard time finding fares that will actually let you travel between the two on NW. It would mean basically SLC-MSP-LAX or SLC-MEM-LAX which are waaay the hell out of the way and probably blow the MPM on any fares between the two cities.