Question

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

Answer 1

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 `-1/m`. If `m=0` then `-1/m` is undefined.

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

`y = 0x+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.