Question

Write the equation of the line perpendicular to 2x+3y=9 that passes through (-2,5). Write your answer in slope-intercept form.

Answer 1

y =
`(3)/(2)` x + 8

Explanation:

the equation of a line in slope intercept form is

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

rearrange 2x + 3y = 9 into this form

subtract 2x from both sides

3y = - 2x + 9 ( divide all terms by 3 )

y = -
`(2)/(3)` x + 3 ← 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)`, hence

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

to find c substitute (- 2, 5) into the partial equation

5 = - 3 + c ⇒ c = 5 + 3 = 8

y =
`(3)/(2)` x + 8 ← equation of perpendicular line