Give geometric representations of y = 3 as an equation (i) in one variable (ii) in two variables

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4. Linear Equations in Two Variables

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Give the geometric representations of $y = 3$ as an equation

$(i)$ in one variable

$(ii)$ in two variables

Option A

Option B

Option C

Option D

Solution

$(i)$ $y =3[$ An equation in one variable $]$

$\because $ $ y =3$ is an equation in one variable, i.e. $y$ only.

$\therefore $ It has a unique solution $y =3$ as shown on the number line shown here.

The unique solution is a point.

$(ii)$ $y =3[$ An equation in two variables]

We can write $y =3$ as

$0x+y=3 $

Now, when $x=1$, $y=3$

when $x=2$, $y=3$

when $x=3$, $y=3$

We get the following table :

$X$	$1$	$2$	$3$
$Y$	$3$	$3$	$3$

Plotting the ordered pairs $(1,\,3)$, $(2,\,3)$ and $(3,\,3)$ on a graph paper, we get a line $AB$ as solution of $0 x + y =3,$ i.e. $y =3$.

Standard 9

Mathematics

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