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# Line A is represented by the line y = 3x − 4. Which of the following

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Joined: 02 Sep 2009
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Line A is represented by the line y = 3x − 4. Which of the following  [#permalink]

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29 May 2018, 21:36
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Difficulty:

15% (low)

Question Stats:

86% (01:30) correct 14% (01:47) wrong based on 82 sessions

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Line A is represented by the line y = 3x − 4. Which of the following represents the equation of a line that is perpendicular to Line A and that travels through point (1,2)?

A. y = −3x + 4

B. y = −x/3 + 4/3

C. y = −3x + 3/4

D. y = −x/3 + 7/3

E. y = −x/3 − 4

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Re: Line A is represented by the line y = 3x − 4. Which of the following  [#permalink]

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29 May 2018, 21:45
1
Bunuel wrote:
Line A is represented by the line y = 3x − 4. Which of the following represents the equation of a line that is perpendicular to Line A and that travels through point (1,2)?

A. y = −3x + 4

B. y = −x/3 + 4/3

C. y = −3x + 3/4

D. y = −x/3 + 7/3

E. y = −x/3 − 4

Don't need to recall the formulae for perpendicular lines. Just test the answer choices whether they travel through point $$(1,2)$$.

After checking, we can find out that only $$y = −x/3 + 7/3$$ travels through point $$(1,2)$$.

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Tulkin.

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Joined: 04 Jan 2015
Posts: 2466
Line A is represented by the line y = 3x − 4. Which of the following  [#permalink]

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29 May 2018, 22:40
1

Solution

Given:
• Line A is represented by y = 3x – 4

To find:
• The equation of the line which is perpendicular to Line A ang travels through point (1, 2)

Approach and Working:
If the equation of Line A is given as y = 3x – 4,
• Slope of Line A = 3
• Slope of the line perpendicular to Line A = $$\frac{-1}{3}$$
[as the product of slopes of two perpendicular lines is -1]

As the perpendicular line passes through (1, 2), we can write
• $$2 = \frac{-1}{3} * 1 + c$$
Or, $$c = \frac{7}{3}$$
• Therefore, the equation of the line which is perpendicular to line A:
$$y = \frac{-1}{3}x + \frac{7}{3}$$

Hence, the correct answer is option D.

[Note: Obviously answer can also be determined by replacing the value in the given options]
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Re: Line A is represented by the line y = 3x − 4. Which of the following  [#permalink]

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31 May 2018, 15:15
Bunuel wrote:
Line A is represented by the line y = 3x − 4. Which of the following represents the equation of a line that is perpendicular to Line A and that travels through point (1,2)?

A. y = −3x + 4

B. y = −x/3 + 4/3

C. y = −3x + 3/4

D. y = −x/3 + 7/3

E. y = −x/3 − 4

A line perpendicular to a line with the equation y = 3x - 4 has a slope of -1/3. We can eliminate answer choices A and C.. Let’s substitute (1,2) into B, D and E.

B. y = −x/3 + 4/3

2 = -1/3 + 4/3

No

D. y = −x/3 + 7/3

2 = -1/3 + 7/3

2 = 2

Yes

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Line A is represented by the line y = 3x − 4. Which of the following  [#permalink]

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31 May 2018, 18:27
Tulkin987 wrote:
Bunuel wrote:
Line A is represented by the line y = 3x − 4. Which of the following represents the equation of a line that is perpendicular to Line A and that travels through point (1,2)?

A. y = −3x + 4
B. y = −x/3 + 4/3
C. y = −3x + 3/4
D. y = −x/3 + 7/3
E. y = −x/3 − 4

Don't need to recall the formulae for perpendicular lines. Just test the answer choices whether they travel through point $$(1,2)$$.

After checking, we can find out that only $$y = −x/3 + 7/3$$ travels through point $$(1,2)$$.

Hi,

Remembering the formula, one can easily to crossout A and C, this can save some time. And what if it were a 700 GMAT question and test makers would throw to you a bunch of options which include (1,2)? Try to leverage all assets in given questions.

P.S. I have no doubt that you remember the formula, yet I was trying to stress the right attitude, which will gain you another 30-40 points on your exam.
Line A is represented by the line y = 3x − 4. Which of the following &nbs [#permalink] 31 May 2018, 18:27
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