| 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. |
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