Quasi-Linear Functions
The indifference curves are not "parallel", as they are not straight lines. They are however shifted, that is they are supposed to maintain vertical distance regardless of the value of $x$. 

The curves you map maintain horizontal distance regardless of $y$. That is because the non-linear variable here is $y$, not $x$. The curves are still shifted, but along the other axis. 

Taking the logarithm of the utility function you get
$$
x + \ln y
$$
which is more clearly quasi linear.