Question

What are the equations of 2 lines that are perpendicular to the line: `4x+y-2 = 0`?

Answer 1

`y = 1/4 x + b`

(`b` can be any number)

Explanation:

Lets rewrite the equation `4x+y-2=0` to solve for y.

`4x+y-2=0`
`4x+y=2`
`y=-4x+2`

This new equation now fits into the helpful format `y=mx+b`

With this formula `b` is equal to the y intercept and `m` is equal to the slope.

So if our slope is `-4` then to calculate a perpendicular line we flip the number and change the sign. So `-4/1` becomes `1/4`.

We can now construct a new equation with the new slope:

`y =1/4 x +2`

That is a perfectly acceptable answer to this question, and to easily generate more equations we can simply change the y intercept to any number we want.

`y =1/4 x +2`
`y =1/4 x +10`
`y =1/4 x - 6`