Question

Draw the graphs of the equations given below

(i) x + y = 2 (ii) 3x $-$ y = 0 (iii) 2x + y = 1

Answer 1

(i)
The equation of the given line is x + y = 2.

x + y = 2

⇒ y = 2 − x .....(1)

Putting x = 0 in (1), we get

y = 2 − 0 = 2

Putting x = 2 in (1), we get

y = 2 − 2 = 0

Putting x = −1 in (1), we get

y = 2 − (−1) = 2 + 1 = 3

Putting x = 5 in (1), we get

y = 2 − 5 = −3

These values can be represented in the table in the form of ordered pairs as follows:

x	0	2	−1	5
y	2	0	3	−3
(x, y)	(0, 2)	(2, 0)	(−1, 3)	(5, −3)

Plot these points on the graph paper.



The line is the graph of the equation x + y = 2.

(ii)
The equation of the given line is 3x − y = 0.

3x − y = 0

⇒ y = 3x .....(1)

Putting x = 0 in (1), we get

y = 3 × 0 = 0

Putting x = 1 in (1), we get

y = 3 × 1 = 3

Putting x = −1 in (1), we get

y = 3 × (−1) = −3

Putting x = 2 in (1), we get

y = 3 × 2 = 6

These values can be represented in the table in the form of ordered pairs as follows:

x	0	1	−1	2
y	0	3	−3	6
(x, y)	(0, 0)	(3, 0)	(−1, −3)	(2, 6)

Plot these points on the graph paper.



The line is the graph of the equation 3x − y = 0.

(iii)
The equation of the given line is 2x + y = 1.

2x + y = 1

⇒ y = 1 − 2x .....(1)

Putting x = 0 in (1), we get

y = 1 − 2 × 0 = 1 − 0 = 1

Putting x = 1 in (1), we get

y = 1 − 2 × 1 = 1 − 2 = −1

Putting x = −1 in (1), we get

y = 1 − 2 × (−1) = 1 + 2 = 3

Putting x = 2 in (1), we get

y = 1 − 2 × 2 = 1 − 4 = −3

These values can be represented in the table in the form of ordered pairs as follows:

x	0	1	−1	2
y	1	−1	3	−3
(x, y)	(0, 1)	(1, −1)	(−1, 3)	(2, −3)

Plot these points on the graph paper.



The line is the graph of the equation 2x + y = 1.