Suppose that a curve is given as the graph of a function, "y" = "f"("x"). To find the tangent line at the point "p" = ("a", "f"("a")), consider another nearby point "q" = ("a" + "h", "f"("a" + "h")) on the curve. The slope of the secant line passing through "p" and "q" is equal to the difference quotient

As the point "q" approaches "p", which corresponds to making "h" smaller and smaller, the difference quotient should approach a certain limiting value "k", which is the slope of the tangent line at the point "p". If "k" is known, the equation of the tangent line can be found in the point-slope form:

Intuitive description
Normal line to a curve
How the method can fail
Surfaces and higher-dimensional manifolds