A graph on a dark blue board with axes x and y and a pink curve, y = f(x). Two gold points on it, (a, f(a)) and (b, f(b)), are joined by a blue secant line. A gold tangent line lies along the curve at the lower point. A fainter, closer secant shows the secants heading to it as the second point slides in.

The average is the slope of a secant, a line through two points. The rate right now is the slope of a tangent: slide the secant's second point closer, and the tangent is the line those secants head to.

A graph of f(x) = x² on axes x and y with x ticks at 1 and 3. A blue secant joins the points (1, 1) and (3, 9) and is marked slope 4. A gold tangent at (3, 9), the line the secants head to as their second point slides in, is marked slope 6.

The blue secant is the average between two points. The gold tangent is the rate right at the later point. They are different lines. (On this teaching screen: from 1 to 3 the secant slope is (9 + (−1)) ÷ 2 = 4; right at 3 the tangent slope is 6.)