Slopes / Tangents Visualized, with Two Points


This blogpost is short, and about slopes. If you’re a STEM or high-school student, and struggle to grasp this notion, or you just want to have yet another intuition for this concept, this article’s for you !


I’d initially made this simulation for a STEM student struggling with his foundations in “function geometry”.
So I tried this 2 points approach.

Slopes are in functions

You may know that slopes are mostly a function-thing. They can represent the rate of change at a point, and thus, are closely tied to derivatives.

Slope = Tangent

If you don’t feel quite confident about slopes, think of tangent lines in geometry !

Slope = Change

If you still don’t feel confident, think of it as change. The slope, on a mountain at a point represents how much higher you’re going if you go forward.
But how much do you have to go forward ? What’s the slope describing ? The top of the mountain, or the closest centimetre ?
It’s where math comes in. With slope, we’re interested in the smallest unit of distance away.
So we’re looking at a point infinitely close to you, in front of you, and looking at how uphill it is, right ?
You can test this by tracing a ling between the two points, and see how close to horizontal it is.

The Simulation

Here’s a preview.

If you want to toy around with it, click the link and alter the hardcoded values as much as you want :)