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Slope. Slope: In mathematics, the slope or gradient of a line is a number that describes the direction of the line on a plane. [1] Often denoted by the letter m, slope is calculated as the ratio of the vertical change to the horizontal change ("rise over run") between two distinct points on the line, giving the same number for any choice of points.
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 alignment is the route of the road, defined as a series of horizontal tangents and curves. The profile is the vertical aspect of the road, including crest and sag curves, and the straight grade lines connecting them. The cross section shows the position and number of vehicle and bicycle lanes and sidewalks, along with their cross slope or ...
In two dimensions, the equation for non-vertical lines is often given in the slope–intercept form: = + where: m is the slope or gradient of the line. b is the y-intercept of the line. x is the independent variable of the function y = f(x).
This proof is valid only if the line is neither vertical nor horizontal, that is, we assume that neither a nor b in the equation of the line is zero. The line with equation ax + by + c = 0 has slope - a / b , so any line perpendicular to it will have slope b / a (the negative reciprocal).
The word horizontal is derived from the Latin horizon, which derives from the Greek ὁρῐ́ζων, meaning 'separating' or 'marking a boundary'. [2] The word vertical is derived from the late Latin verticalis, which is from the same root as vertex, meaning 'highest point' or more literally the 'turning point' such as in a whirlpool.
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 solid diagonal lines are the light cones for the observer's current event, and they intersect at that event. The small dots are other arbitrary events in the spacetime. The slope of the world line (deviation from being vertical) is the velocity of the particle on that section of the world line.