pv=nrt but how we get  pv = kt why?

we know that

pressure

P = (1/3).(N/V)mv².....................(1)

and also 

energy

(1/2)mv² = (3/2)kT

or

mv² = 3kT......................(2)

so, we get (1) as

P = (1/3).(N/V). [3kT]

or

P = (N/V).kT

so, finally

PV = NkT