Linear Equation

Linear Equation

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation’s graph will always be a straight line.

A linear equation is an algebraic equation in which each term has an exponent of 1, and which, when plotted on a graph, always yields a straight line. It is called a “linear equation” .

Both linear equations with one variable and those with two variables exist. Let’s use the examples below to understand how to distinguish between linear and nonlinear equations.

Y = 8x – 9 Linear

Y = x² – 7 Non-Linear, the power of the variable x is 2

√y + x = 6 Non-Linear, the power of the variable y is ½

Y + 3x – 1 = 0 Linear

Y2 – x = 9 Non-Linear, the power of the variable y is 2

Linear Equation Formula

A linear equation is  expressed using a linear formula. There are several ways to accomplish this. A linear equation, for instance, can be written in standard form, slope-intercept form, or point-slope form. Now that we have learned how a linear equation is stated, let’s look at its standard form. We can see that it fluctuates depending on the number of variables, and it is important to keep in mind that all of the variables in the equation should have a degree of 1 as their maximum (and only) value.

Linear Equation Graph

While the graph of a linear equation with two variables, x and y, creates a straight line, the graph of a linear equation with just one variable, x, forms a vertical line which is parallel to the y-axis.

Definition 

• Linear Equations in One Variable

A linear equation with one variable is one that has just one variable. It has the formula Ax + B = 0, with A and B being any two real integers and x being an ambiguous variable with just one possible value. The simplest approach to represent a mathematical statement is in this way. The degree in this equation is always equal to one.

Example:- 3x + 6 = 18.

• Linear Equations in Two Variables

A linear equation with two variables has the formula Ax + By + C = 0, where A, B, and C are all real integers and x and y are the two variables with degrees of 1 each. Such two linear equations are referred to as simultaneous linear equations. 

Example:- 5x + 4y + 10 = 0 

Example

Solve this linear equation: 3x – 2 = 4.

To prevent the equilibrium from being upset, we execute mathematical operations on the left-hand side (LHS) and the right-hand side (RHS). So let’s increase both sides by 2 to get the LHS down to 3x. The equilibrium won’t be thrown off by this. The new RHS is 4 + 2 = 6, and the new LHS is 3x – 2 + 2 = 3x. Let’s now multiply both sides by 3 to get the LHS down to x. As a result, x = 2. One method for resolving linear equations in one variable is as shown above.

Conclusion

In the coordinate system, linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., just one variable). Multiple variables may be present in a linear equation. Linear equations with two variables.

The solution or root of a linear equation is the value of the variable that determines whether the equation is true. If the same number is added, subtracted, multiplied, or divided into both sides of a linear equation, the result remains unchanged.A linear equation with one or two variables has a graph that is always a straight line.