—slopingly, adv. —slopingness, n./slohp/, v., sloped, sloping, n.v.i.1. to have or take an inclined or oblique direction or angle considered with reference to a vertical or horizontal plane; slant.2. to move at an inclination or obliquely: They sloped gradually westward.v.t.3. to direct at a slant or inclination; incline from the horizontal or vertical: The sun sloped its beams.4. to form with a slope or slant: to slope an embankment.5. slope off, Chiefly Brit. Slang. to make one's way out slowly or furtively.n.6. ground that has a natural incline, as the side of a hill.7. inclination or slant, esp. downward or upward.8. deviation from the horizontal or vertical.9. an inclined surface.10. Usually, slopes. hills, esp. foothills or bluffs: the slopes of Mt. Kilimanjaro.11. Math.a. the tangent of the angle between a given straight line and the x-axis of a system of Cartesian coordinates.b. the derivative of the function whose graph is a given curve evaluated at a designated point.12. Slang (disparaging and offensive). an Asian, esp. a Vietnamese.[1495-1505; aphetic var. of ASLOPE; akin to SLIP1]Syn. 1. SLOPE, SLANT mean to incline away from a relatively straight surface or line used as a reference. TO SLOPE is to incline vertically in an oblique direction: The ground slopes (upward or downward) sharply here. TO SLANT is to fall to one side, to lie obliquely to some line whether horizontal or perpendicular: The road slants off to the right.
* * *Numerical measure of a line's inclination relative to the horizontal.In analytic geometry, the slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it ("slope equals rise over run"). In differential calculus, the slope of a line tangent to the graph of a function is given by that function's derivative and represents the instantaneous rate of change of the function with respect to change in the independent variable. In the graph of a position function (representing the distance traveled by an object plotted against elapsed time), the slope of a tangent line represents the object's instantaneous velocity.
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