Different Forms of Linear Equation

A linear equation is one in which the variable’s maximum power is one(1). It’s also known as a one-degree equation. A linear equation in one variable is written in the usual form Ax + B = 0. x is a variable, A is a coefficient, and B is a constant in this equation. A linear equation with two variables can be written in the form of:  Ax + By = C. A and B are coefficients, while C is a constant in this equation.

Definition of Linear Equation

A linear equation is an equation with the maximum degree of the equation as 1. This shows that in a linear equation, no variable has an exponent greater than one(1). A graph of the linear equation is always formed as a straight line. A linear equation is an algebraic equation in which each term has an exponent of one and when graphed, the result is always a straight line. This is why it is termed as a ‘linear equation’. Linear equations with one variable and linear equations with two variables exist. A linear equation is an algebraic equation in which the highest exponent of the variable is one. One, two, or three variables are not included in any linear system with three equations. A system of linear equations normally has just one solution, but it can potentially have none or an infinite number.

Form of Linear Equation

A mathematical equation that defines a line is known as a linear equation. Each line corresponds to an unlimited number of equations, but each linear equation corresponds to precisely one line. A variable with the maximum power in these equations will be 1. Slope-intercept form, point-slope form, and standard form are the three primary types of equations. These equations provide enough information about the line for us to graph it simply.

The different form of linear equation is;

• Standard Form
• Point Slope Form
• Slope Intercept Form

Let us understand each form of linear equation in details;

Standard Form

Constants and variables are combined in linear equations.  We can readily solve systems of equations using the usual form. It’s easy to line up the variables and then add and subtract the equations because it only contains whole-number coefficients. There are a few ways we may use to figure out where these equations cross. We can multiply the equations to get the same x coefficients. After that, we may remove the equations to get a one-variable equation with y. The y-value at the place where the two equations cross is found by solving for y.

• A linear equation in 1 variable can be written in standard form as

ax + b = 0, Here a ≠ 0 also x is variable.

For example:  10x + 5 =0

• The standard form of a 2-variable linear equation can be written as

ax + by  + c= 0, Here a ≠ 0 also x, y are variable.

For example:  10x + 5y + 2 =0

A 3-variable linear equation can be expressed in standard form as

ax + by + cz + d = 0, Here a ≠ 0 also x, y, z is variable.

For example:  10x + 5y + 2z + 1 =0.

Point Slope Form

The point-slope form, as the name suggests, presents one point in a line and its slope. This is a unique method for assisting with line graphing. However, it is more usually employed to convert a line from a verbal or graphical representation to slope-intercept or standard form.

y = mx + b is a slope-intercept form for linear equations. The slope of the line and the y-intercept are used to represent the linear function in the slope-intercept form.

y=mx + b.

Here m is termed as the slope and b is the y-intercept.

Slope Intercept Form

A straight-line equation is generated by finding the points in the x-y plane in this form of linear equation, such that:

y – y1 = m (x – x1), where (x1, y1) is the point’s coordinates. y = mx + y1 – mx1 is another way of expressing it.

Even if the line graph is provided, we must still compute the slope. It’s advisable to utilize one of the spots where the line crosses the y-axis as one of the points used to compute the slope. The values may then be directly entered into the slope-intercept equation. The slope-intercept form can be obtained from the point-slope equation if the y-intercept is not obvious.

Conclusion: 

• A mathematical equation that defines a line is known as a linear equation.
• The following are the several types of linear equations:

• Standard Form 
• Point Slope Form
• Slope Intercept Form