How to Solve the Equation of a Tangent Line

A detailed tutorial on the solving of the equation of a tangent line. Step by step tutorial including several examples of how to solve the equation of a tangent line for reference.

A tangent line is the straight line to a curve at any given point that just touches the curve at that point. In a mathematical sense, at that point the tangent line is going in the same direction as the curve. To solve the equation of a tangent line, say that the curve is the graph of the function y = f(x). The point at which the tangent line intersects the curve is p = (a, f(a)). Now, take another point on the curve that is close to the line, which can be expressed as q = (a + h, f(a + h)). The secant line passes through both of these points, and the slope of the secant line is equal to the difference quotient. The difference quotient is expressed as:

Those who have already studied limits will recognize the difference quotient to be the definition of a limit function.

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