Well, you could simply build an 11x14 frame and put the slate piece in the rabbet, back it up with some foamcore or coroplast and fasten it down with framer's points. I guess you aren't going to use any glass on it. I wouldn't, it would lose the texture and luster of the slate if you put it behind glass.
Another method you could use is to make a backing board out of a lighter gray than the slate (for contrast) and about an inch larger in dimensions on all sides than the slate, that would be about a 13x16 piece of matboard such as Artique Nickel (A4849). Back up the matboard with a piece of coroplast to use for the mounting of the slate.
Now, you cut a couple of lengths of brass rod, bend them to fit over the edges of the slate in about 4 places, (like the bottom left corner, bottom right corner for downward support, and the top left and right side corners for sideways support to minimize shifting left or right.) You could add more rods if you wanted but this would be the minimum I would use.
Edit: After re-reading how much the slate weighs, I would go for 3 or 4 rods across the bottom for downward support and maybe one in each upper side corner and one in the middle of each side and also the middle of the top.)
Punch holes through the matboard and coroplast where the rods are to be positioned, and open up those flutes where the holes go through the coroplast for an inch or so. (These will serve as glue wells later on to hold the rods in place.) The rods will be bent into some shape of a "Z", the top of the "Z" holding the slate in place, the leg of the "Z" passing through the matboard and coroplast, and the bottom of the "Z" fitting into those opened flutes on the coroplast. Everything should fit fairly tight so the slate doesn't shift around.
Now take a glue gun and starting at the bottom of the slate, fill an opened flute with hot melt glue while holding that "Z" rod in place. Let it cool and go on to the other bottom support. Do the same. Do this for all the support rods that you have deemed necessary to hold the piece in place. It doesn't take more than 1/8" of rod bent over the face of the slate to hold it in place. You can make the bottom of the "Z" supports (the part that is glued into the open flutes of the coroplast) an inch or more long as you desire.
If you wanted to hide the brass rod, use some black heat shrink tubing available from Radio Shack and shrink a small piece of it over the brass rod on the matboard side of the mount.
When done, you can mount this into any frame such as an LJ 395254 Ferrosa Iron, an LJ 300240 Java, or an LJ 210285 Tribeca for some examples. Any frame that is deep enough to allow the thickness of the slate, matboard, and coroplast should work fine.
This will give you a nice looking semi-float mount look with a contrasting lighter gray matboard border around the slate.
Framerguy