Not related. An induction motor's speed is related to the frequency of the supply.
However, the rotor always slips slightly so turns slightly slower than the rotating field.
For example a 50Hz 4-pole motor the field rotates at 1500rpm but the motor rotates at about 1380rpm. With increasing load the slip will increase.
It is this slip that induces currents into the rotor. So it will slip even with no load.
With reduced supply voltage this slip will be greater and it will be unable to sustain a load (will slip more at less load).