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Slope

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Slope is a measure of the change in the dependent variable for a given change of the independent variable of a function. The average slope, or slope of the secant line between x1 and x2, can be computed using the formula: . When a linear equation (with no powers other than one and zero) is written in slope-intercept form (), the slope is , the coefficient of . To find the instantaneous slope of a function, or the slope of the tangent line at x0, the limit as x approaches x0 can be taken. This can be extended to every point on a curve by the formula which is the definition of the derivative of f(x). Slopes are an editing feature supported by some Doom source ports which allows the designer to make surfaces that are at angles other than horizontal or vertical. Sloped surfaces in a 2.5D system have issues that are mostly irrelevant in true 3D engines such as Quake. A full implementation of sloped surfaces includes changes to both the renderer and the physics code. The former is relatively simpler than the latter, since even slight changes in the physics code risk breaking demo compatibility. In the context of a filter, refers to how sharply the filter reduces or eliminates frequencies past its cutoff frequency. Slopes are usually expressed either in dB per octave, or in "poles", where one pole equals 6 dB/octave. (The terminology comes from electrical engineering; one "pole" is the equivalent of a single passive RC filter circuit. The word "pole" refers to the mathematical equations which describe the behaviors of filters; the subject is far too complex to get into here.)

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In the context of a filter, refers to how sharply the filter reduces or eliminates frequencies past its cutoff frequency. Slopes are usually expressed either in dB per octave, or in "poles", where one pole equals 6 dB/octave. (The terminology comes from electrical engineering; one "pole" is the equivalent of a single passive RC filter circuit. The word "pole" refers to the mathematical equations which describe the behaviors of filters; the subject is far too complex to get into here.) Most filters used in synthesizers are either 12 or 24 dB/octave, and some can be switched between one and the other. The latter, as might be expected, produces a more prominent effect. The cutoff frequency, by definition, is the frequency at which the output of the filter is 3 dB (a just barely noticable decrease in volume) below the level of the passband. This is where the filter is just beginning to actually filter. At one octave away from the cutoff frequency, a four-pole filter (24 dB/octave) has reduced the output to 27 dB below the passband level; this is usually perceived as about 1/4 as loud as the passband. At two octaves away from the cutoff frequency, the output has dropped to 51 dB below, which will probably be difficult to hear without headphones. At three octaves away, the output has dropped to 75 dB below the passband, which will be imperceptible to most listeners unless the listening level is very loud. Slopes are an editing feature supported by some Doom source ports which allows the designer to make surfaces that are at angles other than horizontal or vertical. Sloped surfaces in a 2.5D system have issues that are mostly irrelevant in true 3D engines such as Quake. In a 2.5D map system, depending on the implementation, it can be either floors or walls that are sloped. Doom source ports usually prefer to slope the floors and ceilings, just like, for example, Duke Nukem 3D, as it is technically more efficient. Regardless of the implementation, the greater the angle between the surface and its "normal" (horizontal or vertical) alignment, the more stretched its texture. Source ports may provide mechanisms to alleviate the problem, such as the Sector_Set*Scale specials in ZDoom. A full implementation of sloped surfaces includes changes to both the renderer and the physics code. The former is relatively simpler than the latter, since even slight changes in the physics code risk breaking demo compatibility. Slope is a measure of the change in the dependent variable for a given change of the independent variable of a function. The average slope, or slope of the secant line between x1 and x2, can be computed using the formula: . When a linear equation (with no powers other than one and zero) is written in slope-intercept form (), the slope is , the coefficient of . To find the instantaneous slope of a function, or the slope of the tangent line at x0, the limit as x approaches x0 can be taken. This can be extended to every point on a curve by the formula which is the definition of the derivative of f(x). File:Nuvola apps kbrunch.png This algebra-related article contains minimal information concerning its topic. You can help the Mathematics Wikia by adding to it.