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Exercise 4.4

1. Give the geometric representations of y = 3 as an equation:
(i) in one variable

Sol. –
(i) Given equation is y = 3.

(ii) in two variables.

Sol. –
y = 3 in two variables is 0.x + 1.y – 3 = 0.
⇒  y is 3 and x can take any value.

Therefore, some points on graph are (0, 3), (1,3), (2, 3), etc.
Plotting these points on the graph paper and joining them, we get the required graph (line) as shown in the adjoining figure.

2. Give the geometric representation of 2x + 9 = 0 as an equation:
(i) in one variable

Sol. –
(i) Given equation is 2x + 9 = 0
⇒                      $x = - {9 \over 2}$

(ii) in two variables.

$\Rightarrow x = - {9 \over 2}$
$\left( { - {9 \over 2},0} \right),\left( { - {9 \over 2},1} \right),\left( { - {9 \over 2},2} \right),etc.$