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# Which of the following is an equation of a line that is perpendicular

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Re: Which of the following is an equation of a line that is perpendicular [#permalink]
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.

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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]
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 [ 20.36 KiB | Viewed 1604 times ]

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