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Math Expert
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Re: Which of the following is an equation of a line that is perpendicular [#permalink]
Expert Reply
Given equation:

\(2x + 3y = 4\)

The slope of the above equation = -(coefficient of y/ coefficient of x) = -3/2

As we know, the product of the slopes of the two perpendicular lines is 1.

The slope of the line perpendicular to the given line would be 2/3.

Now, let us check the slope of the lines given:

\(3x - 2y = 4 : Slope = 2/3\)

\(2x - 3y = 4 : Slope = 3/2\)

\(4 - 3x = -2y\); Writing this equation in the standard form : \(2y - 3x = -4 : Slope = 2/3\)

So the slope of equation I and III is 2/3.

The correct answer is D
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Re: Which of the following is an equation of a line that is perpendicular [#permalink]
Bunuel wrote:
Which of the following is an equation of a line that is perpendicular to the line whose equation is 2x+ 3y= 4?

I. 3x— 2y = 4

II. 2x— 3y = 4

III. 4 — 3x= —2y

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III


m1*m2=-1
so m1= -2/3
we need m2=3/2
which is in III. 4 — 3x= —2y & I. 3x— 2y = 4
IMO D
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Re: Which of the following is an equation of a line that is perpendicular [#permalink]
AyushCrackVerbal is this the general formula we can use : The slope of the above equation = -(coefficient of y/ coefficient of x) = -3/2
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Re: Which of the following is an equation of a line that is perpendicular [#permalink]
Expert Reply
Bunuel wrote:
Which of the following is an equation of a line that is perpendicular to the line whose equation is 2x+ 3y= 4?

I. 3x— 2y = 4

II. 2x— 3y = 4

III. 4 — 3x= —2y

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III


Solution to the question is given in the attachment -
Attachments

Slope GMAT.png
Slope GMAT.png [ 20.36 KiB | Viewed 1604 times ]

GMAT Club Bot
Re: Which of the following is an equation of a line that is perpendicular [#permalink]
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Math Expert
94609 posts