Question

Find the equation of the line perpendicular to 2x + 3y = -5 and

passing through (3, -5). Write the equation in standard form.

Answer 1

3x - 2y = 19

Explanation:

y = mx + b

The slopes of perpendicular lines are opposite reciprocals:

`m_(1)`
`m_(2)` = - 1

~~~~~~~~~~~~

2x + 3y = - 5

y = -
`(2)/(3)` x -
`(5)/(3)`

(3 , - 5 )

Slope of perpendicular line is
`(3)/(2)`

y - ( - 5) =
`(3)/(2)` (x - 3)

y + 5 =
`(3)/(2)` x -
`(9)/(2)`

y =
`(3)/(2)` x -
`(19)/(2)`

3x - 2y = 19