# How do you write an equation of a line given the point (2,3) and the m=undefined?

Jun 13, 2015

$x = 2$ is the equation of the line through $\left(2 , 3\right)$ with undefined slope.

#### Explanation:

If slope $m$ is defined, then the equation of a line can be written in the form $y = m x + c$ where $c$ is the intercept with the $y$ axis.

Given two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ on a line, the slope is given by the formula:

$m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

In the case of the line $x = 2$, consider the two points $\left(2 , 0\right)$ and $\left(2 , 1\right)$.

Then $\frac{\Delta y}{\Delta x} = \frac{1 - 0}{2 - 2} = \frac{1}{0}$ which is undefined.