Slope

Illustration of slope

Slope may mean:

• An area of ground that tends evenly upward or downward
• The degree to which a surface tends upward or downward
• The ratio of the vertical and horizontal distances between two points on a line

Slope Media

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  Slope: m = \frac{\Delta y}{\Delta x} = \tan(\theta)

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  Slope illustrated for y = (3/2)x − 1. Click on to enlarge

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  Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2

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  Slopes of parallel and perpendicular lines

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  At each point, the derivative is the slope of a line that is tangent to the curve at that point. Note: the derivative at point A is positive where green and dash–dot, negative where red and dashed, and zero where black and solid.

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  The illusion of a paradox of area is dispelled by comparing slopes where blue and red triangles meet.

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  Slope warning sign in the Netherlands

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  Slope warning sign in Poland

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  A 1371-meter distance of a railroad with a 20‰ slope. Czech Republic

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  Steam-age railway gradient post indicating a slope in both directions at Meols railway station, United Kingdom