# Graph of linear equation with two variables

In this post we will learn to plot graph of linear equation with two variables using solved examples.

Let us first revise the basics of linear equation.

## What are linear equation with two variables ?

The equation in which highest power of variable is 1 is called linear equations.

Examples of linear equations;

(a) 2x + 6 = 0

(b) \mathtt{\frac{x}{2} +9=0}

(c) 10x + 3y + 7 = 0

In all the above equations, the highest power of all the terms is 1.

### What are linear equation with two variables ?

The linear equation in which two variables are present are called linear equations with two variables.

Examples are;

(a) x + 5y = 9

Here x & y are two variables.
Highest power of terms is 1.

(b) 10x + 13y = 7

Again x and y are two variable with highest power 1.

## Graph of linear equation with two variables

The graph of linear equation is always a straight line.

Understand that linear equations with two variables have infinite solutions and all the solutions are represented in the straight straight line.

Given below are some examples of linear equation with two variables.

(a) 2x + 5y + 6 = 0

(b) 8x – 11y = 13

Note:
All the points in the straight line represents the solution of the linear equation.

Solution are the points (x , y) which makes left and right side of the equation equal to each other.

## Plotting graph of linear equation of two variables

We already know that graph of linear equation with two variable is always a straight line.

In order to plot straight line, we need at-least two points which can be joined together.

Given below are exact steps to plot the graph of linear equation with two variables.

(a) First arrange the equation in form of y = mx + c

(b) Now find the value of two points (x1, y1) and (x2, y2) using hit and trial method.

(c) Now join the two points with the straight line and you will get the required graph.

You can also check the graph by selecting any random point on the plotted line and check if it is satisfying the equation or not.

Using the above three steps, you can plot the graph of any given linear equation.

I hope you understood the above process, let us see some examples for further understanding.

Example 01
Plot graph of x – y = 5

Solution
Follow the below steps;

(a) Arrange the equation in form of y = mx + c

x – y = 5

y = x – 5

(b) Now find two points using hit and trial method.

Put x = 0 in equation, y = x – 5.

y = 0 – 5

y = -5

Hence, (0, -5) is the first point.

Finding second point.
Put x = 3 in the equation, y = x – 5

y = 3 – 5

y = 3 – 5

y = -2

Hence, (3, -2) is the second point.

(c) Plot the above two points on the graph and join them with straight line.

Plotting (0, -5) and (3, -2) on the graph.

Now joining these two points to get the solution.

Hence, the above straight line represents the equation x – y = 5 .

Example 02
Plot the equation 2x – 3y = 6

Solution
Follow the below steps;

(a) Arrange the equation in form of y = mx + c.

2x – 3y = 6

3y = 2x – 6

\mathtt{y\ =\ \frac{2x-6}{3}}

(b) Find two points that satisfy the equation using hit and trial.

Finding First Point

Put x = 0 in the equation.

\mathtt{y\ =\ \frac{2x-6}{3}}\\\ \\ \mathtt{y\ =\frac{2( 0) -6}{3}}\\\ \\ \mathtt{y\ =\ \frac{-6}{3}}\\\ \\ \mathtt{y\ =\ -2}

Hence, (0, -2) is the first point

Finding the second point.

Put x = 1 in the main equation.

\mathtt{y\ =\ \frac{2x-6}{3}}\\\ \\ \mathtt{y\ =\frac{2( 1) -6}{3}}\\\ \\ \mathtt{y\ =\ \frac{2-6}{3}}\\\ \\ \mathtt{y=\ \frac{-4}{3}}\\\ \\ \mathtt{y\ =\ -1.33}

Hence, (1, -1.33) is the second point.

(c) Plot the above two points on the graph and join them using straight line.

Plotting points (0, -2) and (1, -1.33) on graph.

Now join the two points with straight line to get the required graph.

The above straight line represents the equation 2x – 2y = 6

Example 03
Plot the graph of equation 4x – y = 8

Solution
Follow the below steps;

(a) Represent the equation in form of y = mx + c

4x – y = 8

y = 4x – 8

(b) Find two points that satisfy the equation using hit and trial.

Finding first point.

Put x = 0

y = 4x – 8

y = 4 (0) – 8

y = -8

Hence, (0, -8) is the first point.

Finding second point

Put x = 1

y = 4 (1) – 8

y = 4 – 8

y = -4

Hence, (1, -4) is the second point.

(c) Plot the two points on graph and join them with straight line.

Plotting (0, -8) and (1, -4) on the graph.

Joining the two points with straight line we get;

Hence, the above straight line represent equation 4x – y = 8

## Important points of Linear equation graphing

(a) The graph of linear equation with two variables is always a straight line.

(b) Each point on the graph represents the solution of linear equation.

(c) The equation of horizontal x axis and vertical y axis is given as;

X axis equation;
y = 0

Y axis equation;
x = 0

(d) Equation of straight line parallel to y axis is given as;

x = a

(e) Equation of straight line parallel to x axis is given as;

y = a

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