Transfer photos to ICloud

Today I bought 50GB of ICloud storage to transfer my photos which has already occupied 9 GB of my iphone storage.

So I wanted to empty the phone and move all of them to my ICloud storage.

First I thought it’s something that happenes automatically as soon ad I buy ICloud storage. But not only it did not happen, I don’t know how to move them.

How can I move photos from the phone storage to my I cloud to have more space on the phone?

ps: I have Iphone 6 with 32GB and it’s getting slow and hot since it’s full.