1. To recede from something at a downward angle. Our driveway slopes away from the house, so you've got to be careful to always have your handbrake on when you park your car out front. Tell the landscapers to make sure that the grass slopes away from the center of the field. That way, rainwater will naturally drain off into the gutters and we won't be left with big muddy patches.

2. To cause or construct something to recede from something at a downward angle. In this usage, a noun or pronoun can be used between "slope" and "down." I want to slope the floor of the stables away from the horses' stalls so water won't collect beneath them when we bathe them. The builder obviously wasn't paying attention, because he ended up sloping the bookshelf away from the wall.