# 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.

**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.