Question

4. Draw the graph of given equations:
(i) y = x
(ii) 2x+3y=4
(iii) 4x+ 3y = 12
(iv) x -2y = 8 ​

Answer 1

Answer:

It is given

3x−2y=4

We can also write it as

2y=3x−4

y=

2

3x−4

Substituting x=2 in the given equation

y=

2

3(2)−4

So we get

y=

2

6−4

y=

2

2

By division

y=1

Substituting x=−2 in the given equation

y=

2

3(−2)−4

So we get

y=

2

−6−4

y=

2

−10

By division

y=−5

x 2 -2

y 1 -5

Now draw a graph using the points A(2,1) and B(-2,-5)

Join the points AB through a line and extend in both the directions

It is given

x+y−3=0

We can also write it as

y=3−x

Substituting x=1 in the given equation

y=3−1 So we get

y=2

Substituting x=−1 in the given equation

y=3−(−1)

So we get

y=4

x 1 -1

y 2 4

Now draw a graph using the points C(1,2) and D(−1,4)

Join the points CD through a line and extend in both the directions.

Therefore the coordinates of the point where the two graph lines intersect is A(2,1)

solution

Answer 2

Answer:

4x−3y+4=0

⟹x=

4

−4+3y

Let, y=4, then x=

4

−4+3(4)

=2

Similarly, when y=0,x=−1

4x+3y−20=0

⟹x=

4

20−3y

Let, y=4, then x=

4

20−3(4)

=2

Similarly, when y=0,x=5

Plotting the above points on the graph, we get, the intersecting point i.e(2,4)

Area of the region bounded by these lines and x-axis =

2

1

×6units×4 units

=12 sq. units.

solution