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# Which of the following line is parallel to the given line 3x + 4y = 12

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Which of the following line is parallel to the given line 3x + 4y = 12  [#permalink]

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16 Aug 2017, 18:59
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Difficulty:

35% (medium)

Question Stats:

85% (01:03) correct 15% (01:08) wrong based on 13 sessions

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Which of the following line is parallel to the given line 3x + 4y = 12 and has a negative y-intercept.

A. 6x + 9y + 12 = 0

B. 9x + 12y + 36 = 0

C. 9x+ 12y- 36 = 0

D. 6x + 9y + 28 = 0

E. 6x + 9y - 28 = 0

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Which of the following line is parallel to the given line 3x + 4y = 12  [#permalink]

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16 Aug 2017, 20:03
Two lines are parallel if they have the same slope
The side parallel with ax + by = c1 will be ax + by = c2
Since we are given the equation of the first line 3x + 4y = 12, the second line should also have the equation 3x + 4y = c2

Of the answer options, Only Option B(9x + 12y + 36 = 0) and Option C(9x+ 12y- 36 = 0) have equations such that parallel lines can be formed.
Since we need a line which has a negative y-intercept
Consider Option B
9x + 12y = -36 => 3x + 4y = -9 (when dividing by 3)
The y intercept of an equation is when x=0
Let x = 0, we get y = -9/4 (which is a negative y-intercept)
Hence, Option B is our answer
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Re: Which of the following line is parallel to the given line 3x + 4y = 12  [#permalink]

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16 Aug 2017, 22:51
Two lines are parallel if one of the equation is multiple of the other
Option A: 6x is 2*3x but 2*4y is not equal to 9y so wrong.
Thus Option D and E are also wrong
Option B is going to give -36 when transferred to right hand side. (General equation of line is y=mx+c)
Option C is going to give +36.
Since question is asking for negative slope, thus option B is correct
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Re: Which of the following line is parallel to the given line 3x + 4y = 12  [#permalink]

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16 Aug 2017, 23:31
fitzpratik wrote:
Which of the following line is parallel to the given line 3x + 4y = 12 and has a negative y-intercept.

A. 6x + 9y + 12 = 0

B. 9x + 12y + 36 = 0

C. 9x+ 12y- 36 = 0

D. 6x + 9y + 28 = 0

E. 6x + 9y - 28 = 0

Hi...

Get the equation in slope form y=mx+C where m is slope and C is y intercept..
$$3x+4y=12.....Y=3-\frac{3}{4}x$$..

Let's check for slope as -3/4..
Only B and C have slope -9/12=-3/4..
Let's check both B and C..

B. 9x+12y+36=0...
So 12y=-36-9x......Y=-(3/4)x-3..
Here c or y intercept is -3 and slope -3/4.. ANS

C. 9x+12y-36=0..
y=-(3/4)+3..
So slope is same but c is positive..NO

B

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

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Re: Which of the following line is parallel to the given line 3x + 4y = 12   [#permalink] 16 Aug 2017, 23:31
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