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

The given linear equation is
\(\because \) 2x + 9 = 0
\(\Rightarrow x = \frac{-9}{2} \) ...(i)

(i) The representation of the solution on the number line is shown in the figure below, where x = \( \frac{-9}{2} \) is treated as an equation in one variable.




ii)The representation of the solution on the number line is shown in the figure below, where 2x + 9 = 0 can be written as an equation in of two variable i.e., 2x + (0).y = -9

Here, if we observe, all the values of y are permissible as (0).y is always going to be 0.

However, x always has to satisfy the equation to 2x + 9 = 0.

Hence, graph of x = \(\frac{-9}{2} \) will be a line parallel to y-axis and at a distance of \(\frac{-9}{2} \) units along negative x- axis.