There are three levels of visualization to be gleaned from this illustration. The segments themselves give a low-resolution picture of the family of curves which satisfy the differential equation. Secondly, the solution curves can be viewed with the click of a button. Finally, a set of tracing points can be sent along their respective curves, illustrating the concept of initial values. The sketch is simple, but it covers the basics in a way that any visual learner will appreciate. The sketch works nicely when dy/dx is a function of x, but if dy/dx is implicitly defined, the construction is more complex and the differential equation is not easily changed.
Keywords: slope fields, direction fields, anti-derivative, anti-differentiation, integral curves, solution curves, family of solutions, differential equations, dy/dx