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Give the geometric representations of $2x + 9 = 0$ as an equation
$(i)$ in one variable
$(ii)$ in two variables
Solution
$(i)$ $2 x +9=0[$ An equation in one variable $]$
We have : $2 x+9=0 \Rightarrow 2 x=-9 \Rightarrow x=\frac{-9}{2}$
which is a linear equation in one variable ${ }^{\prime} x ^{\prime}$ only. Its solution is the point $\frac{-9}{2}$ on the number line as shown below.
$(ii)$ $2 x +9=0$ [An equation in two variables]
We can write $2 x+9=0$ as $2 x+0 y+9=0$ or $2 x=-9+0 y$
or $x=\frac{-9+0 y}{2}$
$\therefore$ When $y =1, \quad x =\frac{-9+0(1)}{2}=\frac{-9}{2}$
When $y=2, \quad x=\frac{-9+0(2)}{2}=\frac{-9}{2}$
When $y=3$ $x=\frac{-9+0(3)}{2}=\frac{-9}{2}$
Thus, we get the following table :
| $x$ | $\frac{-9}{2}$ | $\frac{-9}{2}$ | $\frac{-9}{2}$ |
| $y$ | $1$ | $2$ | $3$ |
Now, plotting the ordered pairs $\left(\frac{-9}{2},\,1\right),\,\,\left(\frac{-9}{2},\, 2\right),$ and $\left(\frac{-9}{2}, \,3\right)$ on a graph paper and joining them, we get a line $PQ$ as solution of $2 x +9=0$.
