can rearranging a function cause the graph of that function to change?

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this is a very beginner graph question. If I have the function: $\frac{x}{\left(y-2\right)}\le1$

the graph (via Desmos) looks like this:

enter image description here

If I rearrange the function by multiplying both sides by $y-2$ I get this function: $x\le y-2$

The graph of it looks like this:

enter image description here

I don't understand why the graphs might look different, since I'm just rearranging the functions. Please help me understand what I'm doing incorrect.

Thanks