Suppose you begin a bike ride 7km north of your town, and then ride along a straight trail which leads to a park 3km west of town. Write parametric equations expressing your motion with the town being represented by the origin and t=0 represents the starting point and then give the coordinates of your location after 5 minutes using these equations. Eliminate the parameter to get a rectangular equation for this linear path and verify algabraically and graphically that both equations have the same line. Finally, suppose you ride your bike back along the same path, but now t=0 represents the new starting point. What changes if any take place in the parametric and rectangular equations?
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