It started in 1988 when Suzuki switched to a new type of semi flat side carburetor (known as "slingshot" carbs). If I recall correctly, the engine was also given a shorter stroke, and the bike kind of inherited the "slingshot" name.
If its an '85, then technically it is NOT a "slingshot" GSX-R. Although in the guys defense, the original line of GSX-R's are still referred to by many as "slingshot". Its more of generic nick name the whole line inherited, and many people dont know that.
Hope that helps,