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Using the diagram and summing the incident branches into x 1 this equation is seen to be satisfied. As all three variables enter these recast equations in a symmetrical fashion, the symmetry is retained in the graph by placing each variable at the corner of an equilateral triangle. Rotating the figure 120° simply permutes the indices.
Conversely, every line is the set of all solutions of a linear equation. 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 ...
The best known plots of the Michaelis–Menten equation, including the double-reciprocal plot of / against /, [2] the Hanes plot of / against , [3] and the Eadie–Hofstee plot [4] [5] of against / are all plots in observation space, with each observation represented by a point, and the parameters determined from the slope and intercepts of the lines that result.
A log–log plot of y = x (blue), y = x 2 (green), and y = x 3 (red). Note the logarithmic scale markings on each of the axes, and that the log x and log y axes (where the logarithms are 0) are where x and y themselves are 1. Comparison of linear, concave, and convex functions when plotted using a linear scale (left) or a log scale (right).
A linear function is a polynomial function in which the variable x has degree at most one: [2] = +. Such a function is called linear because its graph, the set of all points (, ()) in the Cartesian plane, is a line. The coefficient a is called the slope of the function and of the line (see below).
In three-dimensional Euclidean space, these three planes represent solutions to linear equations, and their intersection represents the set of common solutions: in this case, a unique point. The blue line is the common solution to two of these equations. Linear algebra is the branch of mathematics concerning linear equations such as:
Domain coloring plot of the function f(x) = (x 2 − 1)(x − 2 − i) 2 / x 2 + 2 + 2i , using the structured color function described below. In complex analysis, domain coloring or a color wheel graph is a technique for visualizing complex functions by assigning a color to each point of the complex plane. By assigning points on the ...
For example, the projective curve of equation x 2 + y 2 − z 2 is the projective completion of the unit circle of equation x 2 + y 2 − 1 = 0. This implies that an affine curve and its projective completion are the same curves, or, more precisely that the affine curve is a part of the projective curve that is large enough to well define the ...
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