Question

How do you write an equation of the line perpendicular to the line x - 3y = 9 and passing through the point (3,5)?

Answer 1

I found: `y=-3x+14`

Explanation:

Your perpendicular line musta have a slope `m_1` given as:
`m_1=-1/m` where `m` is the slope of your given line.
Your line can be written as:
`y=x/3-3`
The slope of your given line is equal to the numerical coefficient of `x`, i.e., `m=1/3`.
With this in mind the slope of the perpendicular will be: `m_1=-3`.
We can now use the general relatonship:
`y-y_0=m_1(x-x_0)` to find the equation of the perpendicuar line;
with your data:
`y-5=-3(x-3)`
`y=-3x+9+5`
`y=-3x+14`