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

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Math Expert
Joined: 02 Sep 2009
Posts: 52294
Which of the following lines is perpendicular to 4x + 5y = 9 on the xy  [#permalink]

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15 Jul 2018, 07:30
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2
00:00

Difficulty:

15% (low)

Question Stats:

75% (00:30) correct 25% (01:09) wrong based on 126 sessions

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

A. $$y = \frac{5}{4}x + 2$$

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

C. $$y = -4x + \frac{9}{5}$$

D. $$y = \frac{4}{5}x + \frac{-4}{5}$$

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

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Re: Which of the following lines is perpendicular to 4x + 5y = 9 on the xy  [#permalink]

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15 Jul 2018, 07:44
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4x + 5y = 9
y = -4/5*x + 9/5
Slope of the line = -4/5

So, line perpendicular to the given line should have a slope of 5/4.

A. $$y = \frac{5}{4}x + 2$$

Hence, A.
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Re: Which of the following lines is perpendicular to 4x + 5y = 9 on the xy  [#permalink]

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28 Aug 2018, 04:40
whats the level of this question?
Does this kind of question come on real Gmat ?
Math Expert
Joined: 02 Sep 2009
Posts: 52294
Re: Which of the following lines is perpendicular to 4x + 5y = 9 on the xy  [#permalink]

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28 Aug 2018, 05:05
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Ratnaa19 wrote:
whats the level of this question?
Does this kind of question come on real Gmat ?

According to the 61 sessions (timer attempts) from our users, the difficulty is sub-600. You can check the difficulty of a question in the tags just above the first post.

To answer your other question, yes it's a perfectly valid GMAT question which falls into Coordinate Geometry category.

24. Coordinate Geometry

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Re: Which of the following lines is perpendicular to 4x + 5y = 9 on the xy  [#permalink]

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30 Aug 2018, 17:04
Bunuel wrote:
Which of the following lines is perpendicular to 4x + 5y = 9 on the xy plane?

A. $$y = \frac{5}{4}x + 2$$

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

C. $$y = -4x + \frac{9}{5}$$

D. $$y = \frac{4}{5}x + \frac{-4}{5}$$

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

We need to first express the given line in slope-intercept form, which is y = mx + b, where m is the slope of the line:

5y = -4x + 9

y = (-4/5)x + 9/5

We see that the slope of the given line is -4/5. Since the slopes of two perpendicular lines are negative reciprocals of each other, then a line perpendicular to the given line will have a slope of 5/4. The line whose equation is given in choice A has that slope.

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Re: Which of the following lines is perpendicular to 4x + 5y = 9 on the xy &nbs [#permalink] 30 Aug 2018, 17:04
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