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

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Bunuel
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Which of the following is an equation of a line that is perpendicular [#permalink] New post   31 May 2019, 01:30
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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
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D
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LeoN88
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Re: Which of the following is an equation of a line that is perpendicular [#permalink] New post   31 May 2019, 01:40
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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


For y=mx + c, Two lines are perpendicular provided their slopes: m1*m2= -1

Slope of given line: (-2/3)
Slope of lines:
I (3/2)
II (2/3)
III (3/2)

So only I and III satisfies m1*m2= -1.
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Re: Which of the following is an equation of a line that is perpendicular [#permalink] New post   31 May 2019, 03:42
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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


Linear equation
y = mx + c (where, m is slope and c is constant/y-intercept)

Let's find the slope of the line in question,
2x+3y=4
y= (-2x+4) / 3
slope= -2/3

For perpendicular line, slope is of opposite sign and reciprocal

Let's analyze statements
St. 1
3x— 2y = 4
y = (-3x+4) / (-2)
Slope = 3/2

St.2
2x— 3y = 4
y = (-2x+4) / (-3)
Slope = 2/3

St. 3
4 — 3x= —2y
y = (-3x+4) / (-2)
Slope = 3/2

Only St. 1 & 3 have opposite signs and are reciprocal of -2/3

Option D is the answer
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Re: Which of the following is an equation of a line that is perpendicular [#permalink] New post   31 May 2019, 05:59
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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] New post   31 May 2019, 07:50
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] New post   11 Jul 2021, 01:38
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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SSG12
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Re: Which of the following is an equation of a line that is perpendicular [#permalink] New post   03 Sep 2021, 11:12
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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 -
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Slope GMAT.png
Slope GMAT.png [ 20.36 KiB | Viewed 1465 times ]

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Re: Which of the following is an equation of a line that is perpendicular [#permalink]
03 Sep 2021, 11:12
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