And what if you just kept getting closer and closer and closer? Well then, the slopes of these secant lines are gonna get closer and closer to the slope of the tangent line at x equals three. And if we can figure out the slope of the tangent line, well then we're in business. Because then we're not talking about average rate of change, we're gonna be talking about instantaneous rate of change, which is one of the central ideas. That is the derivative, and we're going to get there soon. But it's really important to appreciate that average rate of change between two points is the same thing as the slope of the secant line. And as those points get closer and closer together, and as the secant line is connecting two closer and closer points together, as that distance between the points, between the x values of the points approach zero, very interesting things are going to happen.