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
Which of the following lines is perpendicular to \(4x + 5y = 9\) on the \(xy\) plane?
This topic has expert replies
\(4x + 5y = 9\)
\(y = -\dfrac{4}{5}x + \dfrac{9}{5}\)
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