Question

What is the equation of the line passing through `(9,2)` and `(9,14)`?

Answer 1

`x=9`

Explanation:

As it is a line that passes through `(9,2)` and `(9.14)`, when either abscissa or ordinate is common, we can easily find the equation of the line - as it will of the form `x=a`, if abscissa is common and of the form `y=b`, if ordinates are common.

In the given case, abscissa is common and is `9`, hence equation is `x=9`.

Answer 2

`x=9`

Explanation:

Gradient `->("change in y")/("change in x")`

Let point 1 be:`" "P_1->(x_1,y_1)->(9,2)`
Let point 2 be`" "P_2->(x_2,y_2)->(9,14)`

Notice that there is no change in `x`

This means that the line is parallel to the y axis (vertical)
Put another way: `x` is always 9 and you may allocate any value you wish to `y`

The way to write this mathematically is `x=9`