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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$2x+(0)y=-9$.