What is the difference between direct and inverse proportion?

Work with these two equations.

y = k*x Never mind the k. Call it one or two or anything you like.
The point is that as x gets larger so will y. That's a direct proportion.

y = k/x This one is slight different and a little harder. Call k = 12
y = 12/x Now try a couple of values. Let x = 2
y = 12/2 = 6 Now let x = 4
y = 12/4 = 3

So (read this carefully) as x gets bigger, you gets smaller. That's an inverse relationship.