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we have been covering direct and inverse proportion at school. Are there any other types of proprtion?

We've been coming across questions like:

x is directly proportion to Y

Then I've been told to write

X (the proportion sign, which is like 8 on its side) Y

X=ky

We are then given a value for x and a value for y and asked to work out k. I'm fine with that but I'm wondering why we have to put "k"? Why does that proportion sign turn into "K"?

Also i was looking at the friedmann equation and i saw it had a "k" in it. When i see a physics equation like that will the K usually mean "constant" and will it have something to do with proportion?

thanks _Muddy_