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

Oct 31, 2017

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:

$x = 2$

Oct 31, 2017

$x = 2$

#### Explanation:

The formula for a slope is:

$m = \frac{\Delta y}{\Delta x}$

Saying you have an undefined slope is the same thing as saying you have zero $\Delta x$ (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 $\left(2 , 4\right)$, 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 :)