Question

Give the geometric representation of $y=3$ as an equation in two variables.

Answer 1

In two variables, we have $x$ and $y$ axis.

Hence, writing equation $y=3$ in terms of $x$ and $y$

$y=3$

$\Rightarrow 0+y=3$

$\Rightarrow 0.x+y=3$ .....$\left(1\right)$

Putting $x=0$ in $\left(1\right)$ we get

$0\left(0\right)+y=3$

$\Rightarrow 0+y=3$

$\Rightarrow y=3$

So, the point is $(0,3)$

Putting $x=1$ in $\left(1\right)$ we get

$0\left(1\right)+y=3$

$\Rightarrow 0+y=3$

$\Rightarrow y=3$

So,the point is $(1,3)$

Now if we plot these points on a graph paper we will obtain a line parallel to $x-$ axis

Hence we can say that,in two variables, $y=3$ is a line which is parallel to $x-$axis