Question

What is the equation of the line with an undefined slope and goes through point (2,4)?

Answer 1

See a solution process below:

Explanation:

If the slope of the line is undefined, then, by definition the line is a vertical line.

For a vertical line, the value of `x` is the same for each and every value of `y`.

Because the value of `x` in the point provided in the problem is: `2`

The equation of the line is:

`x = 2`

Answer 2

`x = 2`

Explanation:

The formula for a slope is:

`m = (Deltay)/(Deltax)`

Saying you have an undefined slope is the same thing as saying you have zero `Deltax` (which would render the sloped undefined since you'd be dividing by zero). In simple terms, you have a rise, but no run.

This basically means you have a vertical line: your `y` has no restriction on what it can be, but `x` can only be one fixed value, and so this is what you'd get. Since you need the line to pass through `(2, 4)`, it's equation would necessarily be `x=2` (you do not have a `y` because `y` no longer changes with respect to `x`).

Here's a graphic representation of this:

Hope that helped :)