Draw the graph of each of the following linear equations in two variables:
(i) x + y = 4
(ii) x - y = 2
(iii) y = 3x
(iv) 3 = 2x + y

Solution:

First of all, we can draw a table for different values of x and y, and then with the help of the values, we can plot a graph for each linear equation.

i) x + y = 4

Re-write the equation as y = 4 - x  ---  Equation (1)

By substituting the different values of x in Equation (1), we get different values for y

• When x = 0, we have: y = 4 - 0 = 4
• When x = 2, we have: y = 4 - 2 = 2
• When x = 4, we have: y = 4 - 4 = 0

Thus, we have the following table with all the obtained solutions:

x	0	2	4
y	4	2	0

By plotting the points (0, 4) (2, 2) and (4, 0) on the graph paper and drawing a line joining the corresponding points, we obtain the graph.

The graph of the line represented by the given equation is as shown.

ii) x – y = 2

Re-write the equation as y = x – 2  ---  Equation (1)  

By substituting the different values of x in Equation (1) we get different values for y

• When x = 0, we have y = 0 - 2 = -2
• When x = 2, we have y = 2 - 2 = 0
• When x = 4, we have y = 4 - 2 = 2

Thus, we have the following table with all the obtained solutions:

x	0	2	4
y	-2	0	2

By Plotting the points (0, -2), (2, 0) and (4, 2) on the graph paper and drawing a line joining the corresponding points, we obtain the graph.

The graph of the line represented by the given equation is as shown

 

 

 

 

 

 

 

 

 

 

 

 

iii) y = 3x   ---  Equation (1)

By substituting the different values of x in Equation (1) we get different values for y.

• When x = 0, we have: y = 3(0) = 0
• When x = 1, we have: y = 3 (1) = 3
• When x = -1, we have: y = 3(-1) = -3

Thus, we have the following table with all the obtained solutions:

x	0	1	-1
y	0	3	-3

By Plotting the points (0, 0), (1, 3), and (-1, -3) on the graph paper and drawing a line joining the corresponding points, we obtain the graph.

The graph of the line represented by the given equation is as shown:

iv) 3 = 2x + y

Re-write the equations

y = 3 - 2x  ---  Equation (1)

By substituting the different values of x in Equation (1) we get different values for y

• When x = 0, we have: y = 3 - 2(0) = 3 - 0 = 3
• When x = 3, we have: y = 3 - 2(3) = 3 - 6 = - 3
• When x = -1, we have: y = 3 - 2 (-1) = 3 + 2 = 5

Thus, we have the following table with all the obtained solutions:

x	0	3	-1
y	3	-3	5

By plotting the points (0, 3), (3, -3), and (-1, 5) on the graph paper and drawing a line joining the corresponding points, we obtain the graph.

The graph of the line represented by the given equation is as shown.

☛ Check: NCERT Solutions for Class 9 Maths Chapter 4

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Video Solution:

Draw the graph of each of the following linear equations in two variables: (i) x + y = 4 (ii) x - y = 2 (iii) y = 3x (iv) 3 = 2x + y

NCERT Solutions Class 9 Maths Chapter 4 Exercise 4.3 Question 1

Summary:

The graphs of each linear equations (i) x + y = 4 (ii) x - y = 2 (iii) y = 3x and (iv) 3 = 2x + y are shown by finding different values of x and y and their respective graphs are plotted.

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