Question

How do you write the equation of the family of line that are perpendicular to 4x+3y-1=0?

Answer 1

`y=-3/4x+b`

Explanation:

Rearrange `4x+3y-1=0` to be an explicit function of x:

`y=-4/3x-1/3`

If two lines are perpendicular, then the product of their gradients is `-1`

i.e.

If the gradients are `m_1` and `m_2`:

`m_1*m_2=-1`

`m_2=1/m_1`

Let `\ \ \ \ m_1=-4/3`

Then:

`m_2=1/(-4/3)=-3/4`

Any line of the form:

`y=-3/4x+b`

Will be perpendicular to `\ \ \ \ y=-4/3x-1/3`