Question

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

Answer 1

ANSWER


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



Step-by-step explanation

The line given to us has equation,

`2x + 3y = 9.`

Let us rewrite in slope intercept form to get,


`3y = - 2x + 9`

`\Rightarrow \: y = - (2)/(3)x + 3`

When we compare to

`y = mx + b`
We can see that, the slope

`m_1 =- (2)/(3)`

The slope of the line that is perpendicular this line can be obtained using the relation,


`m_1* m_2=-1`


Thus,



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



`m_2 = -1 * - (3)/(2) = (3)/(2)`



Hence the line in slope intercept form becomes,



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


Since this line passes through

`(-2,5)`
, we substitute it to find the value of

`b.`




`5= (3)/(2) ( - 2)+ b`



`5= - 3+ b`




`b = 5 + 3`



`b = 8`


Hence the slope-intercept form is


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