In the following, we demonstrate this. This is essentially an animation that you can go through step by step. As you click through, you'll see a little pop-up window that explains what you want to look for as you step through each frame in the demonstration. Click here to open the pop-up window for the current frame of the demonstration.
Finally, we can graph all of the level curves in a countour plot, as shown in the figure to the right. Here we've highlighted the level curve corresponding to z = 1 in magenta.