【Slant】 ,  【slope】 ,  【incline】 ,  【lean】  are comparable when they mean to diverge or cause to diverge from a vertical or horizontal line.

【Slant】 carries the sharpest and clearest implication of such divergence of any of these terms but it carries no explicit implication of how great or how little the divergence is; consequently it is accepted generally as the comprehensive term implying a noticeable physical divergence.

【Slope】  is often used interchangeably with  【slant】  , but it is especially likely to be chosen when the reference is to a surface or a side of an elevation (as a hill or a roof) and there is an intent to suggest a gradual divergence from a vertical or horizontal line; thus, "the ground slopes to the left" usually suggests a lack of steepness; "a sloping roof," unless qualified by such adverbs as sharply or steeply , usually implies a gradual 【slant】 .

【Incline】  (see also  【INCLINE】 2 ) carries a stronger implication of bending or tipping or of being bent or tipped; it is therefore especially appropriate not only when human or similar agency is implied but when what is bent or tipped is an immaterial thing (as one’s will, one’s thoughts, or one’s intentions).

【Lean】  differs from  【incline】 in carrying either a stronger implication of a definite directing of the inclination by a human agent or by some shaping or molding force or of a resting or an intent to rest either literally or figuratively against a support.