## Which of the following lines is perpendicular to $$4x + 5y = 9$$ on the $$xy$$ plane?

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### Which of the following lines is perpendicular to $$4x + 5y = 9$$ on the $$xy$$ plane?

by Vincen » Wed Sep 15, 2021 9:04 am

00:00

A

B

C

D

E

## Global Stats

Which of the following lines is perpendicular to $$4x + 5y = 9$$ on the $$xy$$ plane?

A. $$y=\dfrac54x+2$$

B. $$y=\dfrac{-5}{4}x+9$$

C. $$y=-4x+\dfrac95$$

D. $$y=\dfrac45x+\dfrac{-4}5$$

E. $$y=\dfrac{-4}{5}x$$

Source: Manhattan GMAT

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### Re: Which of the following lines is perpendicular to $$4x + 5y = 9$$ on the $$xy$$ plane?

by swerve » Wed Sep 15, 2021 2:51 pm
Vincen wrote:
Wed Sep 15, 2021 9:04 am
Which of the following lines is perpendicular to $$4x + 5y = 9$$ on the $$xy$$ plane?

A. $$y=\dfrac54x+2$$

B. $$y=\dfrac{-5}{4}x+9$$

C. $$y=-4x+\dfrac95$$

D. $$y=\dfrac45x+\dfrac{-4}5$$

E. $$y=\dfrac{-4}{5}x$$

Source: Manhattan GMAT
$$4x + 5y = 9$$
$$y = -\dfrac{4}{5}x + \dfrac{9}{5}$$
Slope of the line $$= -\dfrac{4}{5}$$

Now, if two lines are perpendicular we must have that the product of their slopes must be equal to $$-1$$

So, line perpendicular to the given line should have a slope of $$\dfrac{5}{4}$$ since $$-\dfrac{4}{5} \ast \dfrac{5}{4}=-1$$

Among the given options, A is the only one that satisfies this condition.

Therefore, A

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