Question

PLEASE HURRY

Which equation represents the line that passes through the point
(5, - 1) and is perpendicular to 2x – 3y = 6?

Answer 1

3x + 2y = 13

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

2x - 3y = 6 ( subtract 2x from both sides )

- 3y = - 2x + 6 ( divide all terms by - 3 )

y =
`(2)/(3)` x - 2 ← in slope- intercept form

with slope m =
`(2)/(3)`

Given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((2)/(3) )` = -
`(3)/(2)` , thus

y = -
`(3)/(2)` x + c ← is the partial equation

To find c substitute (5, - 1) into the partial equation

- 1 = -
`(15)/(2)` + c ⇒ c = - 1 +
`(15)/(2)` =
`(13)/(2)`

y = -
`(3)/(2)` x +
`(13)/(2)` ← in slope- intercept form

Multiply through by 2

2y = - 3x + 13 ( add 3x to both sides )

3x + 2y = 13 ← in standard form