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?

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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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