Why isn't slope run over rise?

Question

Why isn't slope run over rise ? Why does run go first in the numerator?

Answer 1

It's all arbitrary mathematical definitions

Because you plot y on the vertical axis and x on the horizontal axis, it's "rise over run." Had you plotted x on the vertical axis and y on the vertical axis, it would still be rise over run, but the "rise" would then be the difference in x coordinates.

IF you want to look at the graph and xy coordinates from a side view, rotate everything 90 degrees, then it would be "run over rise" y=2x has slope 2, as you go horizontally 1, you go up 2. rotate that line 90 degrees clockwise and it's going downhill with slope -1/2, the negative inverse of 2.

What's uphill slope is downhill slope if you run right to left instead of left to right. It's like America & Britain driving on the right side of the road or left side. Or English vs. Hebrew where you read left to right vs. right to left

Up or down, right or left, look at the graph from upside down or clockwise 90 degrees, or 270 degrees, you'll get different "rises over runs" or "runs over rises" whatever you define "rise" or "run' as

run over rise is the inverse of rise over run. Reverse the graph and you can get that if you want. But you can't communicate with other math people. They're tied to their definition, it's over. That's it. No dissent allowed. It's a dictatorship. If you're in Rome, do as the Romans do. If you're in math, slope is rise over run. End of story. The fat lady has sung. As Yogi Berra said, it's not over until it's over, but it really is over. Live with it. Life goes on. Still, Euclid thought it was over. Then came non-Euclidian geometry. People thought it was over with Newtonian gravity. Then came Einstein's relativity. Maybe if it had any meaningful application or theoretic use, run over rise might catch on. But so far, nothing on the horizon. Maybe Dark Matter in the universe will lead to new mathematical concepts, and maybe some version of run over rise might arise. Or runaway even further, like a slave in pre-Civil War's underground railroad. Who knows? Anything is possible Short of the logically impossible.

Meanwhile. Go with the flow. don't rock the boat. Or you might drown. Don't try to swim upstream, if the current is too fast. Don't try to swim up a waterfall. Still waters run deep, but they're still below the rise, not on top.