Two Equal But Different Graphed Equations: x=1 and xy=y

Here is a graph of x=1 and y=1 (also x=y/y and y=x/x):

The lines are perpendicular to each other as expected.

Here is a graph of xy=y and xy=x (which are x=y/y and y=x/x):

The lines are not perpendicular to each other. They are actually parallel to each other. If you think about it, it may be true. If y=0, then xy equals 0, but x=1 is the simplified equation. Also, if xy=y is graphed as y=0, why is xy=x graphed as y=1 and not x=0?

I don’t know if this had been asked before and not 100% sure whether this is a bug or not, but I wanted to post about it.

Here is the graph: x=1 and y=1