Answer:
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 = [tex]\frac{9}{4}[/tex] x + [tex]\frac{5}{4}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{9}{4}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{9}{4} }[/tex] = - [tex]\frac{4}{9}[/tex] , then
y = - [tex]\frac{4}{9}[/tex] x + c ← is the partial equation
To find c substitute (- 9, 3 ) into the partial equation
3 = 4 + c ⇒ c = 3 - 4 = - 1
y = - [tex]\frac{4}{9}[/tex] 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
