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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 line through these two points is perpendicular to the original ...
Specifically, a straight line on a log–log plot containing points (x 0, F 0) and (x 1, F 1) will have the function: = (/) (/), Of course, the inverse is true too: any function of the form = will have a straight line as its log–log graph representation, where the slope of the line is m.
By using homogeneous coordinates, the intersection point of two implicitly defined lines can be determined quite easily. In 2D, every point can be defined as a projection of a 3D point, given as the ordered triple (x, y, w). The mapping from 3D to 2D coordinates is (x′, y′) = ( x / w , y / w ).
The y-intercept point (,) = (,) corresponds to buying only 4 kg of sausage; while the x-intercept point (,) = (,) corresponds to buying only 2 kg of salami. Note that the graph includes points with negative values of x or y , which have no meaning in terms of the original variables (unless we imagine selling meat to the butcher).
On a linear–log plot, pick some fixed point (x 0, F 0), where F 0 is shorthand for F(x 0), somewhere on the straight line in the above graph, and further some other arbitrary point (x 1, F 1) on the same graph. The slope formula of the plot is: = (/) which leads to
Unlike the slope-intercept and intercept forms, this form can represent any line but also requires only two finite parameters, and p, to be specified. If p > 0 , then φ {\displaystyle \varphi } is uniquely defined modulo 2 π .
Given two different points (x 1, y 1) and (x 2, y 2), there is exactly one line that passes through them. There are several ways to write a linear equation of this line. If x 1 ≠ x 2, the slope of the line is . Thus, a point-slope form is [3]
In non-parametric statistics, the Theil–Sen estimator is a method for robustly fitting a line to sample points in the plane (simple linear regression) by choosing the median of the slopes of all lines through pairs of points. It has also been called Sen's slope estimator, [1] [2] slope selection, [3] [4] the single median method, [5] the ...