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Linear Equation


A linear equation is an algebraic equation of the form

 a_1x_1+...+a_nx_n=b,

where the coefficients a_1, ..., a_n and b are constants, and the a_i are not all zero. It involves no products of distinct variables or powers of variables greater than one.

For a nonvertical line in the plane, a linear equation in two variables can be written in slope-intercept form,

 y=mx+b,

where m is the slope and b is the y-intercept. Linear equations can also be written in standard form, intercept form, and other forms.

Equations such as x=3 and y=2 are linear equations of a single variable, and 2x+4y+5z-6=0 is an example of a linear equation with three variables.


See also

Intercept Form, Line, Linear System of Equations, Point-Slope Form, Polynomial, Quadratic Equation, Slope-Intercept Form, Standard Form, Two-Point Form

Portions of this entry contributed by Christopher Stover

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References

Gellert, W.; Gottwald, S.; Hellwich, M.; Kästner, H.; and Künstner, H. (Eds.). VNR Concise Encyclopedia of Mathematics, 2nd ed. New York: Van Nostrand Reinhold, p. 86, 1989.

Referenced on Wolfram|Alpha

Linear Equation

Cite this as:

Weisstein, Eric W., with contributions by Christopher Stover. "Linear Equation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LinearEquation.html

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