The secant line is a line that connects two points on the graph of a function. The tangent line is the line that is basically the slope of a function at a given point. (So secant line is the slope of a line through TWO points, tangent line is slope of a function at ONE point) The derivative finds the slop at any given point on a function. Basically the derivative is the tangent line at ANY point given for the function f(x).