Different Parametric Equations Every line can be described by infinitely many different sets of parametric equations, since any point on the line and any vector parallel to the line can be used to construct the equations. But how can we tell whether two sets of parametric equations represent the same line? Consider the following two sets of parametric equations:
:
(a) Find two points that lie on Line 1 by setting and in its parametric equations. Then show that these points also lie on by finding two values of the parameter that give these points when substituted into the parametric equations for .
(b) Show that the following two lines are not the same by finding a point on and then showing that it does not lie on
