How to find the equation for a line that goes through 2 points without a valid gradient?

Question

i am studying graphs (high school level) and have a task that I cant seem to figgure out.

I need to find the equation for a line that goes through the points (2,4) & (2,1). I have learned the formula to find the gradient a by $ a=\frac {\delta y} {\delta x} $

I then get $ a= \frac{(1-4)}{(2-2)} a= \frac{-3}{0}$

The formula that I have learned to find the equation for a line is

$y-y_1 = a (x-x_1)$

Seing as I cant find a (can't divide by 0) I dont see how I can use this formula.

The book says the answer is supposed to be x=2.

Thank you for your time and help. -Gregg

Answer 1

Thanks to Aretino i got my answer.

The equation for a line paralel to the y axis is $ x = constant $

The constant is were the line crosses the X axis, which in (2,4) and (2,1) is 2.

$ x = constant $ $ x= 2$

Answer 2

The general equation for a line in the plane is better written as $ax+by=c$ or some variety of this. Using instead $y=mx+c$ or some equivalent implies $b\neq 0$, and leaves $b=0$ to be dealt with as a special case. Note that if $b=0, y$ cannot be expressed as a function of $x$, so the second form does apply when you are looking for a linear function rather than a straight line.

This is relatively trivial in two dimensions, but in more than two, the right formulation can save dealing with lots of special cases.