Question

How do you find the slope of a line perpendicular to `3x+y=15`?

Answer 1

Subtracting `3x` from both sides you get: `y = -3x+15`, which is in standard slope-intercept form, with slope `m = -3`.

Any line perpendicular to it will have slope `-1/m = 1/3`

Explanation:

Either just use the answer above, asserting the `-1/m` formula, or show it geometrically as follows:

Starting with `3x+y=15`, first reflect the line in the `45^o` line `x=y`, by swapping `x` and `y`...

`3y+x=15`

Then reflect in the `y` axis by reversing the sign of `x`

`3y-x=15`

These two geometric steps are equivalent to rotating by a right angle centred on the origin.

Next add `x` to both sides to get:

`3y = x + 15`

Finally divide both sides by `3` to get:

`y = 1/3x + 5`

This is in slope-intercept format with slope `1/3`