does a floor have to be level to install tile or can it be slanted?

There can be a slope to the floor. If fact; when tile is used outside there should be enough grade (slant or slope) to allow moisture/water/snow to drain.

Slant - verb (used without object) to veer or angle away from a given level or line, especially from a horizontal; slope.

Slope - verb (used without object) to have or take an inclined or oblique direction or angle considered with reference to a vertical or horizontal plane; slant.

Grade - (also called slope, incline, ... for engineering and aesthetic design factors. Drainage, slope stability, circulation of people and vehicles.