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$u(x,y) = min(2x,y)+ y?$

I don't understand how we can plot it. I know that there's going to be minimum so I am familiar with the cusp shape of perfect complements. But this looks like a quasilinear utility function. So how can I systematically plot it?

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https://www.desmos.com/calculator/m3yzlrz1rs

Here, as you can see when $2x>y$, $U=y+y=2y$ (Right hand side to the line of kink of $2x=y$ and when $2x<y$, $U=2x+y$ So, the Black curve denotes the utility function of 10 level of utility but you can draw for any with the kink line as $2x=y$.

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