A MOSFET can easily be used as a variable resistor. Consider few important parameters before using as a variable resistor.

The main things are:

1. The minimum resistance you need and the RDS(on) of the MOSFET chosen.

2. The MOSFET's behavior in the linear region though it is similar for almost all the MOSFETs.

Now, consider the following characteristic curves of MOSFET,

1. When the VGS is below Vth of the MOSFET, it is in a cut-off mode which means the entire supply voltage appears across MOSFET. It means that now the MOSFET is acting as a open-load with infinite resistance.

2. When you slowly increase the gate voltage the MOSFET slowly starts conducting by entering the linear region where it starts developing voltage across it which we call as VDS . In this region, the MOSFET acts as a resistance of finite value.

3. Now when the MOSFET enters the saturation region, the resistance of the MOSFET is the least and is equal to the RDS(on) of the MOSFET which is mentioned in the circuit.