How Steep is this Hill?

This activity is meant to be an introductory activity for Calculus. It tries to draw out several ideas. 1) that if you zoom into any curve enough it can be approximated by a straight line, 2) to approximate the slope of a curve we can use a straight line and 3) to calculate the slope of that line at any point, we should choose two points on the curve that are very close to each other. Ideally, I envision giving this to students as a homework piece to warm them up for the main lesson on slopes of secants and tangents. This was loosely based on an activity developed by @mathgeek76 https://teacher.desmos.com/activitybuilder/custom/59789aff79b66d769fa31ed6

By David Petro