linear equation

American  

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.

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linear equation British  

noun

1. a polynomial equation of the first degree, such as x + y = 7

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linear equation Scientific  

1. An algebraic equation, such as y = 4 x + 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.

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Etymology

Origin of linear equation

First recorded in 1810–20

Example Sentences

See Examples For:

linear equation

“With one hand I would teach a complicated integral, and with the other hand I’m teaching them how to write a solution to a simple linear equation like 7x − 5 = 9,” she said.

From Los Angeles Times ● Jul. 9, 2026

Despite this complexity, a close approximation of its motion can be captured with a simple linear equation that uses only the launch speed and angle.

From Science Daily ● Dec. 22, 2025

We wrote linear equations in several forms, but it will be most helpful for us here to use the slope-intercept form of the linear equation.

From Textbooks ● May 6, 2020

Algebraically, a linear equation typically takes the form y = mx + b, where m and b are constants, x is the independent variable, and y is the dependent variable.

From Textbooks ● Mar. 27, 2020

A linear equation like 4x – 12 = 0 is extremely simple to solve, and such problems didn’t entertain algebraists for very long.

From "Zero: The Biography of a Dangerous Idea" by Charles Seife