In this figure, we see how secant lines (lines defined through two points on a curve) can be used to approximate a tangent line. In particular, if [math]P[/math] and [math]Q[/math] are two points on the graph of a function [math]f[/math] and if [math]Q[/math] is very close to [math]P[/math], then the secant line through [math]P[/math] and [math]Q[/math] approximates the line tangent to [math]f[/math] through [math]P[/math].[br][br]In the figure, select an example and drag point [math]Q[/math] to see how you can change the secant line. When [math]Q[/math] is very close to [math]P[/math], the secant line becomes very close to the tangent line through [math]P[/math].[br][br]Click "Show details," and you'll see a different way to modify the secant line. In this situation, you control [math]h[/math], which is the horizontal displacement of [math]Q[/math] from [math]P[/math]. When [math]h[/math] gets very close to 0, this makes [math]Q[/math] get very close to [math]P[/math] and once again the secant line approximates the tangent line. Observe how the labels on the axes change. There are two ways to modify [math]h[/math]: in the graphing window you can drag the large green point on the [math]x[/math]-axis, or in the control window you can drag the green slider.