# How do you write the point slope form of the equation given (3,4) and (-7,4)?

Jun 11, 2017

See a solution process below:

#### Explanation:

Because both of the $y$ values are the same this is, by definition a vertical line. A vertical line has the same $y$ value for each and every value of $x$.

The slope of a vertical line, also by definition is $0$:

The point-slope formula states: $\left(y - \textcolor{red}{{y}_{1}}\right) = \textcolor{b l u e}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$

Where $\textcolor{b l u e}{m}$ is the slope and $\left(\textcolor{red}{{x}_{1} , {y}_{1}}\right)$ is a point the line passes through.

We can use this slope and the values from either of the points in the problem to write the point-slope formula as:

$\left(y - \textcolor{red}{4}\right) = \textcolor{b l u e}{0} \left(x - \textcolor{red}{3}\right)$

Or

$\left(y - \textcolor{red}{4}\right) = \textcolor{b l u e}{0} \left(x - \textcolor{red}{- 7}\right)$

$\left(y - \textcolor{red}{4}\right) = \textcolor{b l u e}{0} \left(x + \textcolor{red}{7}\right)$

We can also, write this equation in the generic form of:

$\left(y - \textcolor{red}{4}\right) = \textcolor{b l u e}{0} \left(x + \textcolor{g r e e n}{a}\right)$

Where $\textcolor{g r e e n}{a}$ is an value you want to select.