What is "slope"

Slope \Slope\, a. Sloping. ``Down the slope hills.''
--Milton.

A bank not steep, but gently slope.
--Bacon.

Slope \Slope\, adv. In a sloping manner. [Obs.]
--Milton.

Slope \Slope\, v. t. [imp. & p. p. Sloped; p. pr. & vb. n. Sloping.] To form with a slope; to give an oblique or slanting direction to; to direct obliquely; to incline; to slant; as, to slope the ground in a garden; to slope a piece of cloth in cutting a garment.

Slope \Slope\, n. [Formed (like abode fr. abide) from OE. slipen. See Slip, v. i.]

1. An oblique direction; a line or direction including from a horizontal line or direction; also, sometimes, an inclination, as of one line or surface to another.

2. Any ground whose surface forms an angle with the plane of the horizon.

   buildings the summit and slope of a hill.
   --Macaulay.

   Under the slopes of Pisgah.
   --Deut. iv. 49. (Rev. Ver.).

3. The part of a continent descending toward, and draining to, a particular ocean; as, the Pacific slope.

   Note: A slope, considered as descending, is a declivity; considered as ascending, an acclivity.

   Slope of a plane (Geom.), the direction of the plane; as, parallel planes have the same slope.

Slope \Slope\, v. i.

1. To take an oblique direction; to be at an angle with the plane of the horizon; to incline; as, the ground slopes.

2. To depart; to disappear suddenly. [Slang]

1610s, "inclination," from slope (v.). Meaning "an incline, a slant (of ground)" is from 1620s. Derogatory slang meaning "Oriental person" is attested from 1948.

1590s, "go in an oblique direction," from earlier adjective meaning "slanting" (c.1500), probably from Middle English aslope (adv.) "on the incline" (late 15c.), from Old English *aslopen, past participle of aslupan "to slip away," from a- "away" + slupan "to slip" (see sleeve). From 1709 as "to be in a slanting position;" transitive sense "place in a slanting position" is from c.1600. Related: Sloped; sloping.

1. (context obsolete English) Sloping. adv. (context obsolete English) slopingly n. 1 An area of ground that tends evenly upward or downward. 2 The degree to which a surface tends upward or downward. 3 (context mathematics English) The ratio of the vertical and horizontal distances between two points on a line; zero if the line is horizontal, undefined if it is vertical. 4 (context mathematics English) The slope of the line tangent to a curve at a given point. 5 The angle a roof surface makes with the horizontal, expressed as a ratio of the units of vertical rise to the units of horizontal length (sometimes referred to as run). 6 (context vulgar highly offensive ethnic slur English) A person of Chinese or other East Asian descent. v

2. (label en intransitive) To tend steadily upward or downward.

1. n. an elevated geological formation; "he climbed the steep slope"; "the house was built on the side of the mountain" [syn: incline, side]

2. the property possessed by a line or surface that departs from the horizontal; "a five-degree gradient" [syn: gradient]

3. v. be at an angle; "The terrain sloped down" [syn: incline, pitch]

Algebraic Slope or gradient of a line describes its steepness, incline, or grade, in mathematics.

Slope may also refer to:

• Grade (slope) of a topographic feature or constructed element
• Roof pitch, steepness of a roof
• Slope (album) by Steve Jansen
• A racial slur against Asians

Slope is the debut solo album by drummer Steve Jansen, released in 2007 by Samadhi Sound. The album includes guest musicians and was recorded all over the world.

Jansen said: "With this album I approached composition attempting to avoid chord and song structures and the usual familiar building blocks. Instead I wanted to piece together unrelated sounds, music samples, rhythms and 'events' in an attempt to deviate from my own trappings as a musician."

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. Slope is often denoted by the letter m; there is no clear answer to the question why the letter m is used for slope, but it might be from the "m for multiple" in the equation of a straight line "y = mx + c".

• The direction of a line is either increasing, decreasing, horizontal or vertical.
  • A line is increasing if it goes up from left to right. The slope is positive, i.e. m > 0.
  • A line is decreasing if it goes down from left to right. The slope is negative, i.e. m < 0.
  • If a line is horizontal the slope is zero. This is a constant function.
  • If a line is vertical the slope is undefined (see below).
• The steepness, incline, or grade of a line is measured by the absolute value of the slope. A slope with a greater absolute value indicates a steeper line

Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line. Sometimes the ratio is expressed as a quotient ("rise over run"), giving the same number for every two distinct points on the same line. A line that is decreasing has a negative "rise". The line may be practical - as set by a road surveyor, or in a diagram that models a road or a roof either as a description or as a plan.

The rise of a road between two points is the difference between the altitude of the road at those two points, say y and y, or in other words, the rise is (y − y) = Δy. For relatively short distances - where the earth's curvature may be neglected, the run is the difference in distance from a fixed point measured along a level, horizontal line, or in other words, the run is (x − x) = Δx. Here the slope of the road between the two points is simply described as the ratio of the altitude change to the horizontal distance between any two points on the line.

In mathematical language, the slope m of the line is

$$m=\frac{y_2-y_1}{x_2-x_1}.$$

The concept of slope applies directly to grades or gradients in geography and civil engineering. Through trigonometry, the grade m of a road is related to its angle of incline θ by the tangent function

m = tan(θ)

Thus, a 45° rising line has a slope of +1 and a 45° falling line has a slope of −1.

As a generalization of this practical description, the mathematics of differential calculus defines the slope of a curve at a point as the slope of the tangent line at that point. When the curve given by a series of points in a diagram or in a list of the coordinates of points, the slope may be calculated not at a point but between any two given points. When the curve is given as a continuous function, perhaps as an algebraic formula, then the differential calculus provides rules giving a formula for the slope of the curve at any point in the middle of the curve.

This generalization of the concept of slope allows very complex constructions to be planned and built that go well beyond static structures that are either horizontals or verticals, but can change in time, move in curves, and change depending on the rate of change of other factors. Thereby, the simple idea of slope becomes one of the main basis of the modern world in terms of both technology and the built environment.