Graph Editor: the Basics

The Graph Editor is where you'll find most of the math that you're using to generate animations in After Effects. It's a visual representation of how your value changes over time.

This is not only true for position data, but really any kind of setting or value you can set. It's a great way to add simple, dynamic action to a fade in opacity, you can use it to give organic motion to rain generators, and even to create abstracted, fractal backgrounds relatively easily.

You can manually change the slope over time by adding keyframes with the Pen tool(G).