The linear equation is like any other equation. It is a simple type of equation and is made up of two expressions that are set equal to each other. It contains one variable which can be evaluated by solving the equation. Also, it is equal to the product which is directly proportional to the other. Such equations we can see as an algebraic expression. In coordinate geometry, such equations are frequently used to represent the equation of a straight line in various forms. In this article, we will discuss the linear equation formula with examples. Let us begin!

**Linear Equation Formula**

**Concept of Linear Equations**

We will start off the solving portion of this chapter by solving these as linear equations. A linear equation is an equation which can be written in the form as given below:

- ax + b=0
- where a and b are the numbers and x is a variable. This form is sometimes also called the standard form of a linear equation in coordinate geometry. But note that, most linear equations will not start off in this form.

Straight line equation in coordinate geometry is”

- y = mx + c
- m is the slope of the straight line
- c is the intersect on the y-axis i.e. a constant value.

or

- Ax + By + C = 0
- Where A, B, and C are constants.

Also, the variable may be different from x. Thus we should not get too locked into always seeing an x there.

Source: en.wikipedia.org

**Steps to Solve Linear Equations**

- If a=b then a+c = b+c for any c. It says that we can add a number, c, to both sides of the given equation without changing the equation.
- If a=b then a−c = b−c for any c. It means we can subtract a number, c, from both sides of an equation without loss of generality.
- If a=b then ac =bc for any c. Thus we can multiply both sides of an equation by a number, c, without affecting the equation.
- If a=b then

\(\frac {a}{c} = \frac {a}{c}c=c\frac {b}{c}\) for any non-zero c. Therefore we can divide both sides of an equation by a non-zero number, c, without any loss of generality.

**Process for Solving Linear Equations**

- If the equation contains any fractions then use the least common denominator to clear the fractions.
- Simplify both sides of the equation by clearing out any parenthesis and then further combining like terms.
- Now get all terms with the variable in them on one side of the equations and all constants on the other side.
- If the coefficient of the variable is not unit value then make the coefficient a one.
- We can verify the answer if we wish to check. We verify the answer by substituting the results from the previous steps into the original equation.

## Solved examples for Linear Equation Formula

Q.1 Solve the given linear equation and find the value of variable term x.

50 x + 60 = 110

Solution: Given linear function is

50 x + 60 = 110

Dividing the equation by 10 both sides, we get

5x + 6 = 11

i.e. 5x = 11-6

i.e. 5x = 5

i.e. \(x = \frac{5}{5}\)

i.e. x = 1

Q.2: Example-1 Solve the given linear equation and determine the value of variable term x.

15 x -55 = 20

Solution: Given linear function is:

15 x – 55 = 20

i.e. 15 x = 20 + 55

i.e. 15 x = 75

i.e. \(x = \frac {75}{15}\)

i.e. x = 5

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