Rusty slate tile is usually a combination of several colours--dark grey, coppery brown, light brown and sometimes streaks of green, blue or black. There isn't one single colour that looks just right against this kind of tile. When deciding what paint colour to couple with rusty slate, consider the other colours in use around the room, in addition to the colours you see within the tile.
Very likely the slate tiles will feature a predominance of deep, orange-copper colours. A matching paint colour of the same value (darkness) as the slate tile will blend the slate tile with the paint, creating a working partnership between paint and tile. The colour of the paint does not need to exactly match the copper colours you see in the tile, which will be variable anyway. Remember that this brazen hue is a warm colour, and will create a sense of energy in the room. Copper may be coupled with accents of deep turquoise and warm reddish-browns used sparingly around the room.
While copper creates a warm and cosy feeling in a room, this lighter neutral, made of half grey and half brown, will more easily match the furniture and other colours in the room, while creating a general feeling of calm. Smoky beige is a lighter colour that will recede into the background, while still playing on the strengths of the rusty tile. Smoky beige pairs well with cream used as a trim and accent around the room.
Medium stone grey is not the most exciting or original choice, but it will match well with the slate, as long as there are tones of grey prevalent amongst the rust colour. If the grey in your slate has a bluish cast, look for a grey with overtones of blue. If the grey in your slate has a greenish tone, look for a grey with tones of green. Stone grey can be paired with other, lighter greys and shades of grey-blue or grey-green.
Deep Gray Brown
This colour can be more brown than grey, or grey than brown. It's not the sort of colour that you can paint on any wall in any room and expect good results--it's very dark and heavy. Still, this sophisticated paint can be used in trim or accents, or as an accent wall. This colour is suitable to use in a room that includes dark greys and browns coupled with creams and light greys.