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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, [5] 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.
the slope field is an array of slope marks in the phase space (in any number of dimensions depending on the number of relevant variables; for example, two in the case of a first-order linear ODE, as seen to the right). Each slope mark is centered at a point (,,, …,) and is parallel to the vector
l = slope length α = angle of inclination. The grade (US) or gradient (UK) (also called stepth, slope, incline, mainfall, pitch or rise) of a physical feature, landform or constructed line is either the elevation angle of that surface to the horizontal or its tangent. It is a special case of the slope, where zero indicates horizontality. A ...
Slope stability analysis is a static or dynamic, analytical or empirical method to evaluate the stability of slopes of soil- and rock-fill dams, embankments, excavated slopes, and natural slopes in soil and rock.
During most of the 20th century three models of hillslope evolution were widely diffused: slope decline, slope replacement and parallel slope retreat. Until the 1950s models of hillslope form evolution were central in geomorphology. The modern understanding is that the evolution of slopes is much more complex than the classical models of ...
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 .