Question

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) Write the equation of the line x 3y

Answer 1

`y = -3x + 14`

Explanation:

Required

The equation of line

perpendicular to :
`x -3y =9`

Passes through
`(3,5)`

We have:

`x -3y =9`

Make y the subject

`3y =x - 9`

Solve for y

`y = (x)/(3) - 3`

Compare the above equation to
`y = mx + c`

`m =(1)/(3)` ---- This represents the slope

Since the line is perpendicular to
`x -3y =9`, then its slope is:

`m_2 = -(1)/(m)`

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

`m_2 =-3`

The equation of the perpendicular line is:

`y =m_2(x - x_1) + y_1`

Where:

`m_2 =-3`

`(x_1,y_1) =`
`(3,5)`

So:

`y = -3(x - 3) + 5`

`y = -3x + 9 + 5`

`y = -3x + 14`