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

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Wed Sep 15, 2021 9:04 am

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

Answer: A

Source: Manhattan GMAT

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Source: Beat The GMAT — Problem Solving | Wed Sep 15, 2021 9:04 am

swerve: Legendary Member; Posts: 2545; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

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

Answer: A

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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