Khan’s definition is fine. Karim Kai Ani is being foolish by insisting that “slope is a rate that describes how two variables change in relation to one another.

Khan’s definition is fine. Karim Kai Ani is being foolish by insisting that “slope is a rate that describes how two variables change in relation to one another.” No, that’s a rate of change. A “slope” is a commonly used rate-of-change in which there’s a reasonably clear “rise over run” relationship implied between the variables of interest. But when that relationship isn’t so clearly implied, sensible people don’t try to describe it by calling it a “slope.” Instead, they say what relationship they really care about: Is it the instantaneous rate of change at a specific point? Or at all points along a curve? (Or surface?) Or is it the average rate of change over some interval? Or the weighted average rate of change over some interval of varying density? Or the weighted average rate of change over constant-width intervals centered at certain (or all) points along a curve? Or is it really that they care about—? You get the drift: If you care about rates of change, you’ll use the term “slope” to describe them only when the context implies a clear “rise over run” relationship between the variables of interest. Kahn seems to get this; Karim Kai Ani, not so much.