I think what I did was find a parametric.
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Let's say I knew about parametric equations BEFORE I did all this. Perhaps I would have noticed in the REVERSE order that those formulas also gave the points where a power function has slope 1.
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From a blackpenredpen video, I know x^y=y^x also has a parametric "solution". Maybe there is some geometric property of the curvy part of that line too.
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