If given two parametric equations for a curve, how would you work out an equation for the gradient?

Parametric equations will have both the x and the y coordinates expressed in terms of another paramater, usually t. Gradients of curves are expressed in the form of an equation of dy/dx, in order to work out the gradient from parametric equations, first the student should differentiate the x equation, giving dx/dt. Then differentiate the y equation, giving dy/dt.

To work out dy/dx, from these, it is necessary to multiply the differential of y (dy/dt) by the inverse of the differential of x (dt/dx) so the dt in both equations cancels out and we are left with only x and y. The resulting dy/dx equation is the equation for the gradient of the curve.