I'm not a mathematician, but I think that the initial response by Karim saying that Khan was incorrect about the definition is really nitpicky and petty. Karim is saying that "Rise over run" is how you calculate it, but he claims it's not the definition. Even if it wasn't the precise definition, for most people, rise over run is good enough for a basic understanding.

Khan saying that Karim was wrong, is wrong and actually made him look worse in my eyes. In the video he said "Slope can present rate of change." No, slope is the rate of change. Him saying Karim was wrong about the price vs gigabyte being the inverse if you switch the axes is ridiculous. By definition, you always say the first variable vs the second variable, where the first variable is the y axis and the second is the x. Khan should have left it at that instead of trying to twist things around to make Karim look wrong, it was a poor and transparent attempt at being vindictive.