# How do you write an equation of a line given (2, 5) and has slope undifined?

Jun 20, 2018

$x = 2$

#### Explanation:

$\text{a line with an undefined slope is a vertical line, parallel }$
$\text{to the y-axis and passing through all points with the }$
$\text{same x-coordinate}$

$\text{for this reason it's equation is } x = c$

$\text{where c is the value of the x-coordinate it goes through}$

$\text{given the point } \left(\textcolor{red}{2} , 5\right)$

$\text{the equation is } x = 2$
graph{(y-1000x+2000)=0 [-10, 10, -5, 5]}

Jun 20, 2018

$y = a x + \left(5 - 2 a\right)$ for any $a$

#### Explanation:

Any line is given on the form $y = a x + b$

You want this line to go through (2, 5), i.e. for $x = 2 y = 5$:
$5 = 2 a + b$
Therefore, $b = 5 - 2 a$
The general equation for the line would, therefore, be:
$y = a x + \left(5 - 2 a\right)$

The lines would go like this: