◀ ▲ ▶Branches / Geometry / Analyticgeometry / Proposition: Presentation of a Straight Line in a Plane as a Linear Equation
Proposition: Presentation of a Straight Line in a Plane as a Linear Equation
Let $L$ be a straight line in the number plane $\mathbb R^2.$ Then
 $L$ goes through the origin $(0,0)\in L$ if and only if $L$ is the set of solutions of the homogenous linear equation $\alpha_1x_1+\alpha_2x_2=0$ for some realvalued coefficients $\alpha_1,\alpha_2\in\mathbb R$ which do not both equal zero.
 $L$ does not go through the origin $(0,0)\not\in L$ if and only if $L$ is the set of solutions of the inhomogenous linear equation $\alpha_1x_1+\alpha_2x_2=\beta$ for some realvalued coefficients $\alpha_1,\alpha_2\in\mathbb R$ which do not both equal zero and some real number $\beta\in\mathbb R$, $\beta\neq 0.$
Table of Contents
Proofs: 1
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Definitions: 1
Explanations: 2
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References
Bibliography
 Knabner, P; Barth, W.: "Lineare Algebra  Grundlagen und Anwendungen", Springer Spektrum, 2013