Here is an animation of y=bx for a range of b values. The graph is shown along with a tangent line to the curve at the point (0,1). Notice that the line has a slope of 1 somewhere around 2.7. In fact, the tangent line to y=bx at the point (0,1) has a slope of 1 precisely when b = 2.71828182845904523... . This value is known as e.