# How do you write the equation of a line in slope intercept, point slope and standard form given (2,2) and (2,-3)?

Jan 5, 2018

See a solution process below:

#### Explanation:

First, we can determine the slope of the line:

The slope can be found by using the formula: $m = \frac{\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}}{\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}}$

Where $m$ is the slope and ($\textcolor{b l u e}{{x}_{1} , {y}_{1}}$) and ($\textcolor{red}{{x}_{2} , {y}_{2}}$) are the two points on the line.

Substituting the values from the points in the problem gives:

$m = \frac{\textcolor{red}{- 3} - \textcolor{b l u e}{2}}{\textcolor{red}{2} - \textcolor{b l u e}{2}} = - \frac{5}{0}$

Because we cannot divide by $0$ the slope of the line is undefined. Vertical lines by definition have an undefined slope.

Vertical lines have the property of for each and every value of $y$ the $x$ value is the same. In this problem $x$ is equal to $2$ for both points. Therefore, the equation of this line is:

$x = 2$