What a slope toward an exterior wall actually means
Your floor slopes toward an exterior wall because the edge of your slab on that side has dropped, or in rarer cases the middle has lifted. Either way it's a foundation movement issue, not a flooring one.
The outer edge of a slab is the weak link. It's where soil dries out fastest, where roof water lands, and where the concrete is thinnest and least supported.
Here's the good news and the bad news. Good news: a lot of these slopes stopped moving long ago and only need monitoring plus a cosmetic fix. Bad news: you can't tell a stable slab from an active one just by looking.
That's the whole game with foundations. The slope you can see matters less than the movement you can't. So the first job is figuring out if it's still going.
The usual suspects, ranked
In most cases, a slab sloping toward one exterior wall comes down to soil and water at that wall.
Soil shrinkage is the top cause. In clay-heavy regions, a dry summer pulls moisture out of the ground and the soil physically contracts. The slab edge loses its support and drops.
Drainage is the close second, and honestly it's often the real root of the shrinkage-and-settlement cycle. A downspout dumping right at the corner soaks that soil, then it dries and shrinks harder than the rest. That side settles first.
Plumbing leaks under the slab are less common but nastier. A supply line weeping under the perimeter erodes soil into a void, and the slab settles into the gap. You'll usually catch this with the water meter or a warm patch on the floor.
Then there's the builder's original work. Slabs poured over poorly compacted fill, especially on graded lots, settle unevenly for decades. If your home is on a hillside cut-and-fill site, that's a prime suspect.
And the sneaky one: heave. In expansive clay, the center of the slab can swell upward and fool you into thinking the wall dropped. The fix for heave is nearly opposite the fix for settlement, so getting this right is critical.