Task# Slopes Between Points on a Line

Illustrative MathematicsVaries

The 'change in y divided by the change in x' can be computed for any two points in the plane. Many people who understand and use slope take for granted the fact that the slopes between any two points on a particular line will always be equal--most of us just learned it as a fact. The purpose of this task is to help students understand why the calculated slope will be the same for any two points on a given line. This is the first step in understanding and explaining why it will work for any line (not just the line shown).