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

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

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New post 29 May 2018, 22:36
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A
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C
D
E

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Question Stats:

89% (01:30) correct 11% (02:01) wrong based on 76 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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New post 29 May 2018, 22:45
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 \((1,2)\).

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

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New post 29 May 2018, 23:40
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.

Answer: 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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New post 31 May 2018, 16:15
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

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

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New post 31 May 2018, 19:27
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 \((1,2)\).
Answer: D


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.
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Line A is represented by the line y = 3x − 4. Which of the following &nbs [#permalink] 31 May 2018, 19:27
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