The equation of the line passing through point with slope
*m* is given by .

If you have a differentiable
function *y*=*f*(*x*) and a particular value of *x*, say,
*x*=*c*, then the slope of the tangent line when *x*=*c* is *f*'(*c*).
Since the point on the graph at this value of *x* is (*c*,*f*(*c*), then
the equation of the tangent line is (*y*-*f*(*c*))=*f*'(*c*)(*x*-*c*).

Wed Apr 21 08:17:28 EDT 1999