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555-605 (Medium)|   Coordinate Plane|                           
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The graph of which of the following equations is a straight line that 21 Oct 2015, 21:25
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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


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2015-10-22_0824.png
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A
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The graph of which of the following equations is a straight line that Updated on: 25 May 2020, 13:39
Originally posted by BrentGMATPrepNow on 28 Aug 2017, 13:28.
Last edited by BrentGMATPrepNow on 25 May 2020, 13:39, edited 1 time in total.
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Bunuel

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.

Show Spoiler
Attachment:
2015-10-22_0824.png
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If two lines are parallel, then they have the SAME SLOPE.

The given line passes through the points (0, 2) and (-3, 0)
Applying the slope formula, we get: Slope = (2 - 0)/(0 - -3)
= 2/3

Now take each equation of each line (in the answer choices) and rewrite it in slope y-intercept form: y = mx + b (where m = slope and b = y-intercept)

The rewritten equation that has m = 2/3, will be the correct answer....

A. 3y - 2x = 0...rewrite as y =(2/3)x + 0
DONE!
This line has a slope of 2/3, so it must be parallel with the given line.

Answer: A
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The graph of which of the following equations is a straight line that 22 Oct 2015, 00:09
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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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The graph of which of the following equations is a straight line that 23 Oct 2015, 01:19
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Bunuel

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.

Show Spoiler
Attachment:
2015-10-22_0824.png
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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.

Answer A.
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The graph of which of the following equations is a straight line that 07 Nov 2015, 03:16
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Bunuel

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.

Show Spoiler
Attachment:
2015-10-22_0824.png
Show more

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

Answer: Option A

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 07 Nov 2015, 08:31
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Bunuel

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.

Show Spoiler
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

Answer: Option A

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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hi,
even observation 1 is not necesary....
parallel lines have the same slope so obsn 3 is sufficient..
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The graph of which of the following equations is a straight line that 07 Nov 2015, 08:38
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chetan2u
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Bunuel

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.

Show Spoiler
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

Answer: Option A

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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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.
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The graph of which of the following equations is a straight line that 07 Nov 2015, 09:15
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Engr2012
chetan2u


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.
Show more

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 25 May 2016, 22:16
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Attached is a visual that should help.
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Screen Shot 2016-05-25 at 9.43.21 PM.png [ 61.25 KiB | Viewed 85152 times ]

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The graph of which of the following equations is a straight line that 10 Sep 2016, 17:17
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Here is an algebraic approach :)
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The graph of which of the following equations is a straight line that 30 Dec 2016, 23:09
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Bunuel

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.

Show more

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. :)


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The graph of which of the following equations is a straight line that 25 Jan 2017, 10:15
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Bunuel

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
Show more

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.

Answer: A
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The graph of which of the following equations is a straight line that 17 Jun 2022, 07:03
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Video solution from Quant Reasoning:
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Bunuel

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.

Show Spoiler
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

Answer: Option A

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
Show more


Hello GMATinsight

Please help. I have some doubts about your observations.

Observation1 : How you have identified line is moving upward. I can't see any arrow in the line.

Observation3: How you have identified this? Is this a formula?

Thank you.
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The graph of which of the following equations is a straight line that 08 Nov 2022, 05:27
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Bunuel

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.

Show Spoiler
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

Answer: Option A

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


Hello GMATinsight

Please help. I have some doubts about your observations.

Observation1 : How you have identified line is moving upward. I can't see any arrow in the line.

Observation3: How you have identified this? Is this a formula?

Thank you.
Show more

760Abhi

1) We always observe a line from Left to right. This line is moving upwards when observed from left to right.
2) Slope of Any line \(= \frac{Rise}{Run} = \frac{y_2 - y_1}{x_2 - x_1}\) yes it's a basic about slope and hence a formula

This line is passing through two points (0,2) and (-3,0)
hence Slope \(= \frac{0-2}{-3-0} = \frac{2}{3}\)

I hope this help! :)
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760Abhi
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Bunuel

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.

Show Spoiler
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

Answer: Option A

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


Hello GMATinsight

Please help. I have some doubts about your observations.

Observation1 : How you have identified line is moving upward. I can't see any arrow in the line.

Observation3: How you have identified this? Is this a formula?

Thank you.
Show more

760Abhi

1) We always observe a line from Left to right. This line is moving upwards when observed from left to right.
2) Slope of Any line \(= \frac{Rise}{Run} = \frac{y_2 - y_1}{x_2 - x_1}\) yes it's a basic about slope and hence a formula

This line is passing through two points (0,2) and (-3,0)
hence Slope \(= \frac{0-2}{-3-0} = \frac{2}{3}\)

I hope this help! :)

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It really helps.

Thank you so much for your quick reply.
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↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧



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

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Let's find the slope of line l first. l passes through the points (0,2) and (-3,0) and we know that

Slope of the line passing through the points \((x_1, y_1)\) and \((x_2, y_2)\) is given by, m = \(\frac{y_2 - y_1}{x_2 - x_1}\)
=> m = \(\frac{2 - 0 }{ ( 0 - (-3))}\) = \(\frac{2}{3}\)

We also know that if two lines are parallel then their slopes will be equal
=> Slope of the parallel line will also be \(\frac{2}{3}\)

Now, we need to find which of the lines given in the option choices has slope of \(\frac{2}{3}\)
We know that Slope of a general line ax + by + c = 0 is given by -(Coefficient of x) / (Coefficient of y) = \(\frac{-a}{b}\) = \(\frac{2}{3}\)

=> a can be -2 and b can b can be 3 or a can be 2 and b can be -3 or other choices.
=> line will be -2x + 3y = 0 or 2x - 3y = 0 or 3y - 2x = 0

So, Answer will be A
Hope it helps!

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The graph of which of the following equations is a straight line that 02 Jan 2025, 05:45
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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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The graph of which of the following equations is a straight line that 07 Jan 2026, 02:06
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