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.
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.