# LINEAR EQUATIONS

Definition of Linear Equation

Graph of Linear Equation

Linear Equation in one variable

Linear Equation in two variables

Example of Linear Equation in daily life

__LINEAR EQUATIONS__

In Mathematics, a **Linear Equation** is an equation of combination of variables, coefficient, and constants in which the highest degree of equation is 1. i.e. An equation that has highest degree of 1 is known as Linear Equation.

**There are linear equations in one variable and linear equations in two variables. **

The standard form of linear equation in one variable is Ax + B = 0 where, ‘x’ is variable; ‘A’ is coefficient of x; and ‘B’ is constant.

The standard form of linear equation in two variables is Ax + By = C where, ‘x’ is variable; ‘A’ and ‘B’ are coefficients of x and y respectively; and ‘C’ is constant.

** Definition:** A linear equation is an algebraic equation where each term has an exponent of 1. Therefore we can easily identify equations as linear or non-linear. Non-Linear equations are those where highest power is not 1.

** Graph of linear equation:** The graph of linear equation always forms a straight line.

__Linear Equations in One Variable:__

A linear equation in one variable is an equation in which there is only one variable. It is of the form Ax + B = 0, where A and B are any two real numbers and x is a variable. It has only one solution. It is the easiest way to represent a mathematical statement. The degree of this equation is always equal to 1.

For example, 3x + 7 = 6; 5x + 8 = 0; 2x + 1 = 13

__Linear Equations in Two Variables:__

A linear equation in two variables is of the form Ax + By + C = 0, in which A, B, C are real numbers and x and y are the two variables, each with a degree of 1.

For example, 6x + 2y + 9 = 0; 4x + 4y = 23; 5x + y = 10

__Example of linear equation in daily life:__

If your office is 30 miles, and you have reached at 8 am, and you know that the traffic is moving at 60 miles per hour. To know what time you should leave from home, use this equation

**Time taken = distance/ rate of travel**

t= 30/60 = ½ hour. i.e. To reach the office at 8 a.m., you should leave home at 7: 30 am.