Give the geometric representations of $2x + 9 = 0$ as an equation
$(i)$ in one variable
$(ii)$ in two variables

(N/A) $(i)$ $2x + 9 = 0$ [An equation in one variable]
We have: $2x + 9 = 0 \Rightarrow 2x = -9 \Rightarrow x = -4.5$ or $x = -\frac{9}{2}$.
This is a linear equation in one variable '$x$' only. Its solution is the point $-\frac{9}{2}$ on the number line.
$(ii)$ $2x + 9 = 0$ [An equation in two variables]
We can write $2x + 9 = 0$ as $2x + 0y + 9 = 0$ or $2x = -9 + 0y$.
Thus,$x = \frac{-9 + 0y}{2}$.
For any value of $y$,$x$ will always be $-\frac{9}{2}$.

$x$	$-\frac{9}{2}$	$-\frac{9}{2}$	$-\frac{9}{2}$
$y$	$1$	$2$	$3$

Plotting the points $\left(-\frac{9}{2}, 1\right)$,$\left(-\frac{9}{2}, 2\right)$,and $\left(-\frac{9}{2}, 3\right)$ on a Cartesian plane and joining them,we get a vertical line parallel to the $y$-axis.