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

Sagot :

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

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