ac.commutative algebra - Example of inclusion which is not a finite morphism

Every closed immersion is a finite morphism. Can you give an example of quasi-projective varieties $Xsubset Y$ such that inclusion $Xhookrightarrow Y$ is not finite? Same with Y projective?

Thanks!

Edit: Sorry this question is very simple, I made a mistake asking the question. For a corrected version, check out this one.