At first I thought this would be equivalent to the directional derivative, but it seems that it isn't. I've tried manipulating the average rate of change formula to suit this question but no luck so far. I'm down to my last attempt so any help would be great, thanks.
Might be $$ \frac{1}{\lVert b - a \rVert}\int\limits_a^b f(u) \cdot du $$ for the average change, where $a = (6,1)$ and $b=(7,2)$. And $$ \DeclareMathOperator{grad}{grad} \frac{\partial f}{\partial n} = \left. (\grad f) \right\vert_a \cdot n \\ n = \frac{b - a}{\lVert b - a \rVert} $$ for the instantaneous derivative in direction $n$.