In algebra, linear equations are algebraic equations in which both sides of the equation are polynomials or monomials of the first degree - i.e. each term does not have any variables to a power other than one.
Form and Connection to Analytic Geometry
In general, a linear equation with variables can be written in the form , where is a series of constants, is a series of variables, and is a constant.
In other words, a linear equation is an equation that can be written in the form , where are constants multiplied by variables and is a constant.
For the particular case (single variable equation), the resulting equation can be graphed as a point on the number line, and for the case (resulting in a linear function), it can be graphed as a line on the Cartesian plane, hence the term "linear" equation. This can extended to a general Cartesian n-space, in which the linear equation with the corresponding number of variables can be graphed as an n-1-space - this concept is the idea behind analytic geometry as envisioned by Fermat and Descartes.