Forms of Linear Equation

A linear equation is a two-variable equation with a line as the graph. A linear equation’s graph is a collection of points in the coordinate plane that are all possible solutions to the issue. If all of the variables are real numbers, the equation can be graphed by drawing enough points to see a pattern, then joining them all together.Slope-intercept form, Point-slope form, and Standard form are the three main types of linear equations.

We will go over the slope-intercept form, the point-slope form, and the standard form will all be covered in this article. 

Linear Equations Definition

Linear equations are first-order equations. Straight lines in the Cartesian plane define these equations. A linear equation is an equation for a straight line. In linear equations, all variables have a maximum order of one.

The following are the other four types or approaches of solving a linear equation:

1. Standard Form.
2. Slope intercept form.
3. Point slope form.

Standard Form

A method of formulating linear equations is the standard form of linear equations. The standard form, the slope-intercept form, and the point-slope form are all ways to write a linear equation. The general form of linear equations is Ax + By = C, which is also known as the standard form.

For example:

Because the maximum power of both variables x and y is 1, the equation 4x + y = 6 is a linear equation. Ax + By = C is the conventional form of a linear equation, where A, B, and C are integers, and x and y are variables.

Linear Equations in One Variable in Standard Form

An equation with only one variable is referred to as a “linear equation in one variable. “It denotes that this linear equation has only one solution. One-variable linear equations are written in the standard form as follows:

Ax + B = 0

A and B are both integers, and x is the only variable.

For example, the typical form of a linear equation with a single variable is 3x + 6 = 12, and there is only one solution for the value of x, which is 4.

Linear Equations in Two Variables: Standard Form

There are two solutions to a two-variable linear equation. In two variables, the standard form of linear equations is written as,

Ax + By = C

A,B, and C are integers, but x and y are variables.

Slope Intercept Form

The slope intercept form of a straight line is one of the most common ways to express its equation. Consider the case where we are given the slope of a line and we know it crosses the y-axis somewhere in the cartesian plane. It’s best to utilise the slope intercept form in these situations.

We used the usual notation Ax + By = C to write linear equations 

The slope of the line and the y-intercept are used to express the linear function in the slope-intercept form.

y = mx + b 

where, The slope is m, and the y-intercept is b.

Point Slope Form

The point slope form is used to obtain the equation of a straight line that passes through a given point and is inclined at a certain angle to the x-axis.

The point slope form is used to find the equation of a line whose slope is ‘m’ and passes through a point (x₁,y₁,  ). The equation of a straight line can be expressed in a variety of ways. The point slope shape is one of them. The point slope form’s equation is:

y – y₁= m(x – x₁)

(x, y) is a random point on the line, and m is the line’s slope.

Conclusion

We observed in this article that, the linear equation works in the same way as any other equation. It’s a simple sort of equation that consists of two expressions that are set to the same value. It has a single variable that may be determined by solving the equation. It’s also the same as the product, which is proportional to the other. We can think of such equations as algebraic expressions. Such equations are commonly used in coordinate geometry to express the equation of a straight line in various ways.