(geometry) The slope of the secant line passing through the points \left( a, \, f(a) \right) and \left( a+h, \, f(a+h) \right). As the horizontal distance h>0 between the points approaches zero, the slope of this secant line approaches the slope of the tangent line to f(x) at x=a, which is equal to the derivative of f(x) at x=a.