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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.
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 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 ...
Vertical tangent on the function ƒ(x) at x = c. In mathematics, particularly calculus, a vertical tangent is a tangent line that is vertical. Because a vertical line has infinite slope, a function whose graph has a vertical tangent is not differentiable at the point of tangency.
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).
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). Let ( m , n ) be the point of intersection of the line ax + by + c = 0 and the line perpendicular to it which passes through the point ( x 0 , y 0 ).
The slope of the secant line passing through p and q is equal to the difference quotient (+) (). As the point q approaches p, which corresponds to making h smaller and smaller, the difference quotient should approach a certain limiting value k, which is the slope of the tangent line at the point p.
If the slope is =, this is a constant function = defining a horizontal line, which some authors exclude from the class of linear functions. [3] With this definition, the degree of a linear polynomial would be exactly one, and its graph would be a line that is neither vertical nor horizontal.
A vertical line is any line parallel to the vertical direction. A horizontal line is any line normal to a vertical line. Horizontal lines do not cross each other. Vertical lines do not cross each other. Not all of these elementary geometric facts are true in the 3-D context.