Slope

on . Posted in Algebra

Slope, abbreviated as m, is a measure of how steep a line is.  It is typically used to describe the incline or gradient of a straight line in a two-dimensional Cartesian coordinate system.  The slope quantifies the rate at which one variable (usually denoted as "y") changes with respect to changes in another variable (usually denoted as "x").  In words, the slope is the ratio of the change in the vertical direction (y) to the change in the horizontal direction (x) between two points on the line.  A slope is a line between two points, x1, y1 and x2, y2.

common ways to express slope

  • Percentage Grade (%)  -  This is the most common method for expressing slope.  It represents the vertical rise or fall over a horizontal distance, expressed as a percentage.
  • Ratio  -  Slope can also be expressed as a ratio, such as 1:20.
  • Angle of Incline  -  Slope can be represented as an angle, usually measured in degrees, minutes, and seconds.  The angle is the arctangent of the ratio of the vertical rise to the horizontal run.

In surveying, accurate measurement and consideration of slope are necessary for designing structures, determining drainage patterns, and ensuring the stability and safety of engineered projects.

 

Slope Formula

\(\large{ m = \frac{y}{x} }\)     (Slope)

\(\large{ y = m \; x }\)

\(\large{ x = \frac{y}{m} }\)

Symbol English Metric
\(\large{ m }\) = slope \(\large{ ft }\) \(\large{ m }\) 
\(\large{ y }\) = rise \(\large{ ft }\) \(\large{ m }\)
\(\large{ x }\) = run \(\large{ ft }\) \(\large{ m }\)

 

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Tags: Hydraulic Surveying