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