how to find drain current and Gate voltage using transfer characterstics
If you want to bias the output at 5V then you need a drain current of about 2.3 mA because 2.3 mA through a 2k2 source resistor produces 5V. The graph in your question is useless for telling you this.

Given also that the data sheet specifies that Vgs(threshold) is typically 2.1 volts for a drain current of 1mA you will need to set the gate voltage at slightly higher than (2.1 + 5) volts. Choose Rg2 to achieve this.

Given that the range of Vgs(threshold) can vary from 0.8 volts to 3 volts there could easily be some sloppiness in what you achieve.

BJTs are much more consistent and if you used (say) a BC547 as an emitter follower, you would be setting the base voltage between 5.5 volts and 5.8 volts. Source followers like this are somewhat problematic.