Write the equation of a line perpendicular to 9x−4y=−5 that passes through the point (−9,3).

4x + 9y = - 9

Step-by-step explanation:

The equation of a line in slope- intercept form is

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

Given

9x - 4y = - 5 ( subtract 9x from both sides )

- 4y = - 9x - 5 ( divide terms by - 4 )

y = x + ← in slope- intercept form

with slope m =

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

= - = - = - , then

y = - x + c ← is the partial equation

To find c substitute (- 9, 3 ) into the partial equation

3 = 4 + c ⇒ c = 3 - 4 = - 1

y = - x - 1 ( multiply through by 9 to clear the fraction )

9y = - 4x - 9 ( add 4x to both sides )

4x + 9y = - 9 ← equation in standard form

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^