## IM Commentary

This task assumes that students are familiar with the $\Delta x$ and $\Delta y$ notations. Students most likely developed this familiarity in their work with slope.

An important property of linear functions is that they grow by equal differences over equal intervals. In F.LE.1a Equal Differences over Equal Intervals 1, students prove this for equal intervals of length one unit, and note that in this case the equal differences have the same value as the slope. In F.LE.1a Equal Differences over Equal Intervals 2, students prove the property in general (for equal intervals of any length).

Instructors should use their judgment as to how many examples students should do on their own (for example, repeating part (c) with several different functions, possibly varying both the slope and the value of $\Delta x$) before attempting to tackle the more general algebraic scenario in part (d).