# How do you write an equation in point slope form that passes through P(-3,-2) and perpendicular to y=3?

Jun 16, 2015

It is not possible to write an equation for the perpendicular line in point-slope form.

It is possible to write it in the form $x = - 3$.

#### Explanation:

In general, if a line has slope $m$, then any perpendicular line will have slope $- \frac{1}{m}$. If $m = 0$ then $- \frac{1}{m}$ is undefined.

The line $y = 3$ is expressible in slope-intercept form as:

$y = 0 x + 3$

The slope is the multiplier of $x$, which is $0$.

It is possible to construct an equation for a perpendicular line by following these steps:

(1) Swap $x$ and $y$ in the original equation. This is equivalent to reflecting the line in the ${45}^{o}$ line $y = x$.
(2) Reverse the sign of the term in $x$ or the term in $y$. This is equivalent to reflection in the $y$ or $x$ axis respectively.

The combination of these two geometrical operations is equivalent to rotating by a right angle.

Starting with $y = 3$, first swap $x$ and $y$ to get $x = 3$, then reverse the sign of $x$ to get $- x = 3$. That is $x = - 3$. This line happens to be satisfied by the given point, but if not, you would just change the constant term to give another parallel line with the same slope.