Coloring Line Art PS Tutorial

Ever wonder how to create rainbow lines? How about creating different colored lines without having to change your brush color for each little section? Or being able to change the line color easily any time you want? This is a quick way of doing it.
This is a beginners tutorial so I tried to make it very visual and explain it simply.
If you are unfamiliar with Photoshop or new with it, I hope this is easily understandable.

EDIT:
I should have said click the gradient tool in the tool bar and go into the options bar (shown above) and apply the preset one that looks like a rainbow.

Stock background by ~Enchantedgal-Stock [link]