Linear Equation

Linear Equation Definition

A linear equation is a mathematical equation that represents a straight line when graphed on a coordinate plane.

In general form, a linear equation can be expressed as $ax+by=c$ , where $x\text{ and } y$ are variables, $a$ , $b$ , and $c$ are constants (with $a$ and $b$ not both equal to zero), and $x$ and $y$ have no exponents or variables multiplied together.

Degree: A linear equation has a degree of 1, meaning the highest power of any variable in the equation is 1.
Straight Line Graph: When graphed, the solutions to a linear equation form a straight line on the coordinate plane.
Variables: A linear equation typically involves two variables, often denoted as $x$ and $y$ , but the general form can be extended to more variables.

Examples of Linear Equations

Simple Linear Equation: $2x+3y=6$ , This equation represents a line on the coordinate plane. The constants are $a=2$ , $b=3$ , and $c=6$ .
Linear Equation with Fractions: $\frac{1}{2}x-3y=4$ , This equation is still linear because the variables have a degree of 1. The constants are $a=\frac{1}{2}$ , $b=\text{-}3$ , and $c=4$ .
Linear Equation with Negative Coefficients: $\text{-}4x+2y=8$ , The equation is linear, and the constants are $a=\text{-}4$ , $b=2$ and $c=8$ .
Linear Equation with One Variable: $3x-2=7$ , Even though it has only one variable, this is still considered a linear equation because the variable $x$ has a degree of 1.
Linear Equation with Three Variables: $2x-y+3z=5$ , Linear equations can involve more than two variables. Here, $x$ , $y$ , and $z$ are the variables.

Linear Equation

Table of Contents

Linear Equation Definition

Examples of Linear Equations

Related Links