| 1. | a first-order equation involving two variables: its graph is a straight line in the Cartesian coordinate system. |
| 2. | any equation such that the sum of two solutions is a solution, and a constant multiple of a solution is a solution. |
| linear equation n. An algebraic equation, such as y = 2x + 7 or 3x + 2y - z = 4, in which the highest degree term in the variable or variables is of the first degree. The graph of such an equation is a straight line if there are two variables. |
| linear equation
An algebraic equation, such as y = 4x + 3, in which the variables are of the first degree (that is, raised only to the first power). The graph of such an equation is a straight line. |
linear equation
statement that a first-degree polynomial-that is, the sum of a set of terms, each of which is the product of a constant and the first power of a variable-is equal to a constant. Specifically, a linear equation in n variables is of the form a0+a1x1++anxn=c, in which x1, , xn are variables, the coefficients a0, , an are constants, and c is a constant. If there is more than one variable, the equation may be linear in some variables and not in the others. Thus, the equation x+y=3 is linear in both x and y, whereas x+y2=0 is linear in x but not in y. Any equation of two variables, linear in each, represents a straight line in Cartesian coordinates; if the constant term c=0, the line passes through the origin
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