1. To slant at an upward angle (to or toward something). It hasn't been too bad cycling to work for the most part, but the road slopes up near the end and I always end up drenched in sweat by the time I get to the office. We've got to make sure the sidewalk slopes up to the entrance of the building so people with mobility issues won't have any problems getting in. The field slopes up toward the base of the mountains, like a gentle invitation to a greater challenge.

2. To cause or construct something to have an upward slant (to or toward something). In this usage, a noun or pronoun can be used between "slope" and "up." Whenever I'm building shelves, I always try to slope them up a tiny bit to help keep things from rolling off. I want to slope the driveway right up to our front door.