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Math Expert V
Joined: 02 Sep 2009
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The graph of which of the following equations is a straight line that  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 65% (01:30) correct 35% (01:49) wrong based on 1783 sessions

HideShow timer Statistics The graph of which of the following equations is a straight line that is parallel to line l in the figure above?

(A) 3y − 2x = 0
(B) 3y + 2x = 0
(C) 3y + 2x = 6
(D) 2y − 3x = 6
(E) 2y + 3x = −6

Kudos for a correct solution.

Attachment: 2015-10-22_0824.png [ 7.95 KiB | Viewed 35048 times ]

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Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

The graph of which of the following equations is a straight line that is parallel to line l in the figure above?

(A) 3y − 2x = 0
(B) 3y + 2x = 0
(C) 3y + 2x = 6
(D) 2y − 3x = 6
(E) 2y + 3x = −6

The graph shows that the line passes (-3,0) and (0,2). So the difference of x is 3(=0-(-3)), the difference of y is 2(=2-0).
The gradient of the line is, therefore, 2/3.

A parallel line should have the same gradient. Among the chioces only (A) has the gradient 2/3 (3y-2x=0 --> 3y=2x --> y= (2/3) x).
So the answer is (A).
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Vyshak wrote:
One of the lines parallel to the given line will have co-ordinates (3,-2). Substitute x = 3 and y = -2. option B satisfies the equation.

the slope of the given line is +ve. so you need another +ve slope line to be parallel to it. Only options A and D have that. Out of which only option a matches with the slope of 2/3 of line l. so A.
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Bunuel wrote: The graph of which of the following equations is a straight line that is parallel to line l in the figure above?

(A) 3y − 2x = 0
(B) 3y + 2x = 0
(C) 3y + 2x = 6
(D) 2y − 3x = 6
(E) 2y + 3x = −6

Kudos for a correct solution.

Attachment:
2015-10-22_0824.png

A line is parallel to line l if it has the same value for m in the formula y=mx+b. So we have to calculate the value of m of the line l in the picture:

y2-y1/x2-x1 = 2-0 / 0-(-3) = 2/3 =m = slope of line l

If you rewrite (A) to y = 2/3x, you see that A has the same slope.

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Re: The graph of which of the following equations is a straight line that  [#permalink]

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I'll go with A.
For the lines to be parallel, the slope must be the same
for the perpendicular lines, the slope of the second line is the negative reciprocal of the slope of the first line. Here, we are looking for a line with the same slope as the drawn line - 2/3
only A has the same slope.
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Bunuel wrote: The graph of which of the following equations is a straight line that is parallel to line l in the figure above?

(A) 3y − 2x = 0
(B) 3y + 2x = 0
(C) 3y + 2x = 6
(D) 2y − 3x = 6
(E) 2y + 3x = −6

Kudos for a correct solution.

Attachment:
2015-10-22_0824.png

Observation 1: Line is upward rising so SLOPE MUST BE POSITIVE

Observation 2: Y-Intercept is +2

Observation 3: Slope = 2(y-intercept) / 3(x-interecpt) = 2/3

Based on "Observation 1" Options B, C and E are ruled out

Now, Options A and D remain

Based on Observation 3, Option D is ruled out which has slope=3/2

P.S. Observation 2 in this question was not necessary as we had to find a line parallel to given line for which Y-Intercept must be different. But these are critical and Primary observations that one must make before starting to solve in question of Co-ordinate Geometry
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The graph of which of the following equations is a straight line that  [#permalink]

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Clearly, the line passes through (0,2) and (-3,0). The slope for this line : 2/3.
A line parallel to this line will have the same slope.
So, option(A) is having the slope as 2/3.

Math Expert V
Joined: 02 Aug 2009
Posts: 7953
Re: The graph of which of the following equations is a straight line that  [#permalink]

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GMATinsight wrote:
Bunuel wrote: The graph of which of the following equations is a straight line that is parallel to line l in the figure above?

(A) 3y − 2x = 0
(B) 3y + 2x = 0
(C) 3y + 2x = 6
(D) 2y − 3x = 6
(E) 2y + 3x = −6

Kudos for a correct solution.

Attachment:
2015-10-22_0824.png

Observation 1: Line is upward rising so SLOPE MUST BE POSITIVE

Observation 2: Y-Intercept is +2

Observation 3: Slope = 2(y-intercept) / 3(x-interecpt) = 2/3

Based on "Observation 1" Options B, C and E are ruled out

Now, Options A and D remain

Based on Observation 3, Option D is ruled out which has slope=3/2

P.S. Observation 2 in this question was not necessary as we had to find a line parallel to given line for which Y-Intercept must be different. But these are critical and Primary observations that one must make before starting to solve in question of Co-ordinate Geometry

hi,
even observation 1 is not necesary....
parallel lines have the same slope so obsn 3 is sufficient..
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Re: The graph of which of the following equations is a straight line that  [#permalink]

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chetan2u wrote:
GMATinsight wrote:
Bunuel wrote: The graph of which of the following equations is a straight line that is parallel to line l in the figure above?

(A) 3y − 2x = 0
(B) 3y + 2x = 0
(C) 3y + 2x = 6
(D) 2y − 3x = 6
(E) 2y + 3x = −6

Kudos for a correct solution.

Attachment:
2015-10-22_0824.png

Observation 1: Line is upward rising so SLOPE MUST BE POSITIVE

Observation 2: Y-Intercept is +2

Observation 3: Slope = 2(y-intercept) / 3(x-interecpt) = 2/3

Based on "Observation 1" Options B, C and E are ruled out

Now, Options A and D remain

Based on Observation 3, Option D is ruled out which has slope=3/2

P.S. Observation 2 in this question was not necessary as we had to find a line parallel to given line for which Y-Intercept must be different. But these are critical and Primary observations that one must make before starting to solve in question of Co-ordinate Geometry

hi,
even observation 1 is not necesary....
parallel lines have the same slope so obsn 3 is sufficient..

It is necessary to rule out B,C,E for their slopes are <0

Either you actually calculate the slope to rule out B,C,E or just look at the positive nature and rule these 3 options out.
Math Expert V
Joined: 02 Aug 2009
Posts: 7953
Re: The graph of which of the following equations is a straight line that  [#permalink]

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Engr2012 wrote:
chetan2u wrote:

hi,
even observation 1 is not necesary....
parallel lines have the same slope so obsn 3 is sufficient..

It is necessary to rule out B,C,E for their slopes are <0

Either you actually calculate the slope to rule out B,C,E or just look at the positive nature and rule these 3 options out.

Hi,
I think its very straight..
if one observation can eliminate all wrong choices, other observations are not necessary..
arent you required to check for slope..
if any other set of line ,other than llel lines, also has property of same slopes, only then you may require to use other obsn to eliminate choices..
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The graph of which of the following equations is a straight line that  [#permalink]

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Another way to look at slope can be to interpret it visually by noticing the transition through its two points (intercepts): when y increased by 2 (from 0 to 2), x increased by 3 (from -3 to 0), therefore slope = 2/3.
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Re: The graph of which of the following equations is a straight line that  [#permalink]

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Bunuel wrote: The graph of which of the following equations is a straight line that is parallel to line l in the figure above?

(A) 3y − 2x = 0
(B) 3y + 2x = 0
(C) 3y + 2x = 6
(D) 2y − 3x = 6
(E) 2y + 3x = −6

Kudos for a correct solution.

Attachment:
2015-10-22_0824.png

Okay here is a very simple solution but you must understand that slope = rise or drop in y axis/run of x axis.(always take absolute value of x)
Now here slope = rise/run=2/3. Parallel line will also have same slope.
Check A bcz it is the easiest to check for. ... well we have a slope of 2/3. We don't even have to look at any other option.
Remember in PS there is only one unique solution to the problem.
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Re: The graph of which of the following equations is a straight line that  [#permalink]

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Attached is a visual that should help.
Attachments Screen Shot 2016-05-25 at 9.43.21 PM.png [ 61.25 KiB | Viewed 27111 times ]

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GMAT 1: 470 Q30 V20 GMAT 2: 620 Q42 V33 Re: The graph of which of the following equations is a straight line that  [#permalink]

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Here is an algebraic approach Attachments Screenshot_20160910-211534.jpg [ 551.22 KiB | Viewed 25649 times ]

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The graph of which of the following equations is a straight line that  [#permalink]

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Bunuel wrote: The graph of which of the following equations is a straight line that is parallel to line l in the figure above?

(A) 3y − 2x = 0
(B) 3y + 2x = 0
(C) 3y + 2x = 6
(D) 2y − 3x = 6
(E) 2y + 3x = −6

Kudos for a correct solution.

From the figure given, we can write the equation of the line l as -
$$\frac{y}{2} +\frac{x}{-3} = 1$$
$$3y - 2z = 6$$

Now any line which is parallel to the above line can be written as 3y - 2z = k where k is any real number.

Therefore we just need to look at the answer options and find an equation which matches the above general form.

And there is only one option 3y - 2z = 0. Hence the correct answer option is A. Thanks,
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Re: The graph of which of the following equations is a straight line that  [#permalink]

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Bunuel wrote: The graph of which of the following equations is a straight line that is parallel to line l in the figure above?

(A) 3y − 2x = 0
(B) 3y + 2x = 0
(C) 3y + 2x = 6
(D) 2y − 3x = 6
(E) 2y + 3x = −6

Kudos for a correct solution.

Attachment:
2015-10-22_0824.png

The slope of the given line in slope-intercept form is y=(2/3)x +4
parallel lines have same slope, so of all the given option only one equation has slope = 2/3.

Hence option A is correct.
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Re: The graph of which of the following equations is a straight line that  [#permalink]

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Bunuel wrote: The graph of which of the following equations is a straight line that is parallel to line l in the figure above?

(A) 3y − 2x = 0
(B) 3y + 2x = 0
(C) 3y + 2x = 6
(D) 2y − 3x = 6
(E) 2y + 3x = −6

Recall that if two lines are parallel, then they have the same slope. Therefore, to solve this problem, we need to find the slope of the given line first. Using the provided diagram, we see that we have points of (-3,0) and (0,2). So we have a slope of:

(change in y)/(change in x) = (0 - 2)/(-3 - 0) = -2/-3 = 2/3

We also see that the y intercept is 2; thus, the equation of line l is:

y = (2/3)x + 2

We can manipulate the equation for line l to look more like the answer choices. We can start by multiplying the entire equation by 3 and we obtain:

3y = 2x + 6

3y - 2x = 6

Since answer choice A is the only answer with “3y - 2x,” we see that 3y - 2x = 0, must be parallel to line l.

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Re: The graph of which of the following equations is a straight line that  [#permalink]

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Using the points (0,2) and (-3,0) in the line equation we get the slope as 2/3 .
While trying to find the slope of given options using what is y/x we see that Option A has slope 2/3.
According to the parallel rule that slope of line 1 =slope of line 2. We can say that Option A is the correct answer
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Re: The graph of which of the following equations is a straight line that  [#permalink]

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Rule 1 - Parallel lines have the same slope.
Rule 2 - If y increases, as x increases then slope is always positive => It means option B,C and E out due to negative slope
slope of line -> y intercept/x intercept => 2/3
so answer is A
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Re: The graph of which of the following equations is a straight line that  [#permalink]

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Check this post for more on the concept of slope: https://www.veritasprep.com/blog/2016/0 ... line-gmat/
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