What's so special about the number e?

The [color=#dd0000][b]line[/b][/color] below passes through [color=#dd0000][b]two points[/b][/color] on the [color=#0000bb][b]graph of [math]y=e^x[/math][/b][/color]. Move the points around. There is a very special relationship between the slope of the line and the location of the points.