I think this debate does sadly just come down to semantics, and I tend to side with Kahn on that merit. Once I got past a certain point in my math education (first half of intro of calculus 1) "slope" wasn't used anymore. We moved to derivatives and gradients. In my education we've always used slope as a purposefully simple/geometric term for 1 dimensional lines plotted in two dimensional x-y planes.
Agreed, "slope" is a rather useless concept beyond algebra. When you're plotting, say, a position function, the slope of the function at any given point is of limited meaningfulness--the velocity, on the other hand, much more so! Likewise, the slope of the velocity curve at any given point is of little import, but the acceleration is very meaningful.
Of course, the slope of the position curve is the velocity; what I'm suggesting is that referring to it as slope detracts from understanding, while referring to it as velocity enhances understanding. Consequently, getting all wrapped around the axle over the canonical definition of slope is a shining example of majoring in the minors.
