# linear equation

## linear equation

noun Mathematics.
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.
Compare linear operator.

Origin:
1810–20

Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
Cite This Source Link To linear equation
Collins
World English Dictionary
 linear equation —n a polynomial equation of the first degree, such as x + y = 7

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
Cite This Source
American Heritage
Science Dictionary
 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.
The American Heritage® Science Dictionary
Cite This Source
Encyclopedia Britannica
Encyclopedia

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

Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.
Cite This Source
Example sentences
Three students' solutions to a linear equation are presented and compared.
Nearby Words