Question

how do you relate the equations for kinetic and potential energy to illustrate the law of conservation of energy?

Answer 1

The conservation of energy is a principle stating that energy cannot be created or destroyed but can be altered from one form to another. With that said. Potential Energy would be like a Rubber band, just sitting there, nothing will happen, however when one picks it up, and stretches it between the fingers, and then lets go of it, Potential energy from the still rubber band becomes Kinetic energy as it flies through the air. 
Kinetic meaning motion. Potential meaning not moving however it has the potential for moving as I described above. Hope this helps.