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# Give the geometric representations of $ 2 x+9=0 $ as an equation

**(i)** in one variable

**(ii)** in two variables.

To do:

We have to write the geometric representation of $2x+9=0$ as an equation

(i) in one variable and

(ii) in two variables.

Solution:

(i) We know that,

To draw a graph of a linear equation in one variable, we need only one solution.

Given,

$2x+9=0$

This implies,

$2x=-9$

$x=\frac{-9}{2}$

$x=-4.5$

Therefore,

$x=-4.5$ and $y=0$

The geometric representation of $2x+9=0$ in one variable is,

(ii) We know that,

To draw a graph of a linear equation in two variables, we need at least two solutions to the given equation.

$2x+9=0$ can be written as,

$2x+(0)y+9=0$ in two variables.

To find the solutions to the equation $2x+(0)y+9=0$

Let us substitute $y=0, 1$ and $x=-4.5$ in equation $2x+(0)y=-9$

We get,

$2(-4.5)+(0)y=-9$

$-9+0=-9$

$-9=-9$

For $y=1$

We get,

$2(-4.5)+(0)1=-9$

$-9+0=-9$

$-9=-9$

Therefore,

$(-4.5, 0)$ and $(-4.5, 1)$ are two solutions of the equation$2x+(0)y=-9$.

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