Question

Draw the graph of each of the following linear equations in two variables: 

(i) x + y = 4 

(ii) x – y = 2 

(iii) -x + y = 6 

(iv) y = 2x 

(v) 3x + 5y = 15 

(vi) x/2 − y/3 = 2 

(vii) (x−2)/3 = y – 3 

(viii) 2y = -x +1

Answer 1

(i) Given : x + y = 4 

or y = 4 – x, 

Find values of x and y: 

Putting x = 0 ⇒ y = 4 

Putting x = 4 ⇒ y = 0 

Graph: 

Mark points (0, 4) and (4, 0) on the graph and join them.

(ii) Given: x – y = 2 

So, y = x – 2 

Putting x = 0 ⇒ y = – 2 

Putting x = 2 ⇒ y = 0 

Graph: 

Mark points (0, -2) and (2, 0) on the graph and join them.

(iii) Given: – x + y = 6 

So, y = 6 + x 

Putting x = 0 ⇒ y = 6

Putting x = -6 ⇒ y = 0 

Graph: 

Mark points (0, 6) and (-6, 0) on the graph and join them.

(iv) Given: y = 2x 

Put x = 1 ⇒ y = 2 

Put x = 3 ⇒ y = 6 

Graph: 

Mark points (1, 2) and (3, 6) on the graph and join them.

(v) Given: 3x + 5y = 15 

Or 5y = 15 – 3x 

Putting x = 0 ⇒ 5y = 15 ⇒ y =3 

Putting x = 5 ⇒ 5y = 0 ⇒ y = 0 

Graph: 

Mark points (0, 3) and (5, 0) on the graph and join them.

(vi) Given: x/2 – y/3 = 2 

3x – 2y = 12 

y = (3x–12)/2 

Putting x = 0 ⇒ y = -6 

Putting x = 4 ⇒ y = 0 

Graph: 

Mark points (0, -6) and (4, 0) on the graph and join them.

(vii) Given: (x −2)/3 = y − 3 

x – 2 = 3(y – 3) x – 2 

= 3y – 9 x 

= 3y – 7 

Now, put x = 5 in x = 3y – 7 

y = 4 

Putting x = 8 in x = 3y – 7, 

y = 5 

Graph: 

Mark points (5, 4) and (8, 5) on the graph and join them.

(viii) Given: 2y = – x +1 

2y = 1 – x 

Now, putting x = 1 in 2y = 1 – x, we get; 

y = 0 

Again, putting x = 5 in 2y = 1 – x, we get; 

y = -2 

Graph:

Mark points (1, 0) and (5, -2) on the graph and join them.