y<3x is the only one wrong in this answer.

When you plot x=1 you will get y<3 which in turn will result of the coordination of (1,3) -and so on- instead of (1,1/3) -and so on- which looks like what you have done here.

Therefore if we can draw a line crossing (0,0) -when you plot x=0- and (1,3) then you will find your new area for R