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Definition Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
Grade (slope) The grade (US) or gradient (UK) (also called stepth, slope, incline, mainfall, pitch or rise) of a physical feature, landform or constructed line refers to the tangent of the angle of that surface to the horizontal. It is a special case of the slope, where zero indicates horizontality. A larger number indicates higher or steeper ...
The phrase "linear equation" takes its origin in this correspondence between lines and equations: a linear equation in two variables is an equation whose solutions form a line. If b ≠ 0, the line is the graph of the function of x that has been defined in the preceding section. If b = 0, the line is a vertical line (that is a line parallel to ...
In statistics, simple linear regression (SLR) is a linear regression model with a single explanatory variable. That is, it concerns two-dimensional sample points with one independent variable and one dependent variable (conventionally, the x and y coordinates in a Cartesian coordinate system) and finds a linear function (a non-vertical straight line) that, as accurately as possible, predicts ...
A slope field (also called a direction field [1]) is a graphical representation of the solutions to a first-order differential equation [2] of a scalar function. Solutions to a slope field are functions drawn as solid curves. A slope field shows the slope of a differential equation at certain vertical and horizontal intervals on the x-y plane ...
The Western Slope is a colloquial term generally understood to describe the part of the state of Colorado west of the Continental Divide. [1] Bodies of water west of the Divide flow toward the Pacific Ocean; water that falls and flows east of the Divide heads east toward the Gulf of Mexico. [2] The Western Slope encompasses about 33% of the ...
Stream gradient (or stream slope) is the grade (or slope) of a stream. It is measured by the ratio of drop in elevation and horizontal distance. [1] It is a dimensionless quantity, usually expressed in units of meters per kilometer (m/km) or feet per mile (ft/mi); it may also be expressed in percent (%). The world average river reach slope is 2 ...
Slope stability refers to the condition of inclined soil or rock slopes to withstand or undergo movement; the opposite condition is called slope instability or slope failure. The stability condition of slopes is a subject of study and research in soil mechanics, geotechnical engineering and engineering geology.