Draw the graph of each of the following equations:
(i) y = x
(ii) y = −x
(iii) y + 3x = 0
(iv) 2x + 3y = 0
(v) 3x − 2y = 0
(vi) 2x + y = 0

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Solution

(i) Given equation: y = x
When x = 0, y = 0.
When x = 1, y = 1.
Thus, we have the following table:

x 0 1

y 0 1

Now, plot the points (0,0) and (1,1).
Join the points and extend the line in both the directions.
The line segment is the required graph of y = x.

(ii) Given equation: y = -x
When x = 0, y = 0.
When x = 1, y = -1.
Thus, we have the following table:

x 0 1

y 0 -1

Now, plot the points (0,0) and (1,-1).
Join the points and extend the line in both the directions.
The line segment is the required graph of y = -x.

(iii) Given equation: y + 3x = 0
When x = 0, y = 0.
When x = 1, y = -3.
Thus, we have the following table:

x 0 1

y 0 -3

Now, plot the points (0,0) and (1,-3)
Join the points and extend the line in both the directions.
Thus, the line segment is the required graph of y + 3x = 0.

(iv) Given equation: 2x+ 3y = 0
When x = 0, y = 0.
When x = 3, y = -2.
Thus, we have the following table:

x 0 3

y 0 -2

Now, plot the points (0,0) and (3,-2).
Join the points and extend the line in both the directions.
The line segment is the required graph of 2x+ 3y = 0

(v) Given equation: 3x - 2y = 0
When x = 0, y = 0.
When x = 2, y = 3.
Thus, we have the following table:

x 0 2

y 0 3

Now, plot the points (0,0) and (2,3).
Join the points and extend the line in both the directions.
The line segment is the required graph of 3x - 2y = 0

(vi) Given equation: 2x + y = 0
When x = 0, y = 0.
When x = 1, y = -2.
Thus, we have the following table:

x 0 1

y 0 -2

Now, plot the points (0,0) and (1,-2)
Join the points and extend the line in both the directions.
The line segment is the required graph of 2x + y = 0.

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