Class 9 RD Sharma Solutions – Chapter 13 Linear Equation in Two Variable- Exercise 13.4

Question 1: Give the geometric representations of the following equations
(a) on the number line (b) on the Cartesian plane:
(i) x = 2 
(ii) y + 3 = 0 
(iii) y = 3 
(iv) 2x + 9 = 0 
(v) 3x – 5 = 0

Solution:

(i) x = 2
The representation of equation on the number line:

The representation of equation on the Cartesian plane:

(ii) y + 3 = 0

or y = -3
The representation of the equation on the number line:

The representation of the equation on the Cartesian plane:

(iii) y = 3
The representation of equation on the number line:

The representation of equation on the Cartesian plane:

(iv) 2x + 9 = 0
or x =  -9 
             2
The representation of equation on the number line:

The representation of equation on the Cartesian plane:

(v) 3x – 5 = 0
or x =  5 
3
The representation of equation on the number line:

The representation of equation on the Cartesian plane:

Question 2: Give the geometrical representation of 2x + 13 = 0 as an equation in
(i) one variable 
(ii) two variables

Solution:

2x + 13 = 0
(i) Isolate given equation in x
Subtract 13 from both the sides
2x + 13 – 13 = 0 – 13
2x = -13
Divide each side by 2
x =  – 13  = -6.5
           2
Which is an equation in one variable.

(ii) 2x + 13 = 0 can be written as 2x + 0y + 13 = 0
The representation of the solution on the Cartesian plane: A line parallel to y axis passing through the point (-13  , 0):
                                                                                                                                                                             2

Question 3: Write the equation of a line passing through the point (0, 4) and parallel to x-axis.

Solution: 

Here, x-coordinate is 0 and y-coordinate is 4, so equation of the line passing through the point (0, 4) is y = 4.

Question 4: Write the equation of a line passing through the point (3, 5) and parallel to x-axis.

Solution: 

Here x-coordinate = 3 and y-coordinate = 5
Since required line is parallel to x-axis, so equation of line is y = 5.

Question 5: Write the equation of a line parallel to y-axis and passing through the point (-3, -7)

Solution:

Here x-coordinate = -3 and y-coordinate = -7
Since required line is parallel to y-axis, so equation of line is x = -3.