Types of equation

In the previous article, we understood what is equation. There are three types of equations that would be useful to you. They are namely, linear equation, quadratic equation, and cubic equation. Each equation has its own set of characteristics. In this article, we will learn about a linear equation and how to draw it.

Linear equation:

Linear equations basically consist of variables and coefficients. They are put together by mathematical operations such as addition and subtraction.

As an example: 2X + 4Y = C 0R 2x + 4y = 8

In this case, the number 2 and the number 4 are referred to as coefficients whereas X and why are variables, and C or 0 is a constant.

Let us take another example:

2x + 4y + 8z = 10

In this case, we noticed that there are three variables. They are X, Y, and Z. Also, we have a numeric value or a constant on the right-hand stopicIde. Thus, we have a set of variables on the left-hand stopicIde and a constant on the right-hand stopicIde.

Similarly, we can have many variables such as A, B, C, P, Q… in a linear equation.

Remember that you can bring the constant 10 which is on the right-hand stopicIde to the left-hand stopicIde too. By doing so, we can make the equation:

2x + 4y + 8z - 10 = 0.

Definition of the linear equation:

An equation is called a linear equation when its algebraic expression has the highest power of the variable which is equivalent to 1. Such a linear equation it’s also called a one-degree equation. 

The other way to understand this is an equation having an algebraic term with an exponent or power of one. 

How does the graph of a linear equation look like?

Since the linear equation has the highest power or exponent which is equivalent to 1, the graph always is a straight line when drawn with X and Y axes. 

If you see the graph, you will notice that when the X versus Y-axis is plotted, we get a straight line.

By looking at the graph you will understand that the straight-line is obtained with the coordinates as (1,1); (2,2), and (3,3).

Here, common points are found out among the three coordinates. When a line is drawn passing through these points, we get a straight line.

How to draw a graph of a linear equation?

Drawing a graph of a linear equation with one variable X on the horizontal axis and another variable Y on the vertical axis is simple. You will have to follow the instructions given below.

Let us take a linear equation with two variables: x - y = 2

This is the simplest example. For plotting the graph for a linear equation x - y = 2, you will have to find the values for the variables X and Y.

⦁ You need to convert the equation of the form y = ax + b. Thus, we get y = x - 2.

⦁ Now, you have to put some values of X and why so as to satisfy the equation x - y = 2.

⦁ Let’s start by putting x = 2. This will make y = 0. Thus, we have the initial coordinate (2,0). This is not at the origin (0,0).

⦁ Now, let us put another value for the value of X. Let x = 4. This will make y = 2. Thus, we have another coordinate (4, 2).

⦁ Let x = 6. This will make y = 4. Thus, we have another coordinate (6,4).

⦁ Let x =8. This will make y = 6. Thus, we have another coordinate (8,6).

The coordinates for the equation x - y = 2 are (2,0), (4,2), (6,4), and (8, 6).

One of the important points to notice by checking out the graph is that there is a straight line that passes through (2,0). It doesn’t pass through the origin (0, 0). It has to be remembered that it is not always necessary that we will always get a line passing through the origin in the case of a linear equation. What matters is, we get a straight line when we draw a graph between the X and Y axes.