Can I move a kitchen drain and tie into existing drain?

I am looking to move a sink on an outside west wall 10 to 11 feet south of the present location. Could I just tie into the existing drain and air stack? Leaving them both where they are now. I figure to raise the new drain end about 3 inches for pitch. The air stack just left as is. Suggestions would be helpful or is this alright? The new location is on the same outside wall it will just go about 10.5 feet to the left. The new location puts things on the street side of the roof ridge line. Current location is the back side of the ridge line. I was thinking about building a false wall to hide the drain where it would show about four feet. The house is on a slab.