Question

How do I write the equation of a line that is perpendicular to `y=3x+4` and goes through the point (3,5)?

Answer 1

`y=-1/3x+6`

Explanation:

Two perpendicular lines have opposite reciprocal slopes.

The slope in `y=3x+4` is `3`, so the line perpendicular to it will have a slope of `-1/3`.

We can write this in the form `y=-1/3x+b` and then plug in `(3,5)` for `x` and `y` to find the equation of the line perpendicular to the line `y=3x+4` that goes through the point `(3,5)`.

`5=-1/3(3)+b`
`5=-1+b`
`6=b`

Therefore, the equation of our new line is: `y=-1/3x+6`.