**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.