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

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Math Expert
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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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

Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:

2015-10-22_0824.png [ 7.95 KiB | Viewed 20114 times ]
[Reveal] Spoiler: OA

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

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21 Oct 2015, 23:22
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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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The graph of which of the following equations is a straight line that [#permalink]

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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).
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"Only $79 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Retired Moderator Joined: 29 Apr 2015 Posts: 874 Location: Switzerland Concentration: Economics, Finance Schools: LBS MIF '19 WE: Asset Management (Investment Banking) Re: The graph of which of the following equations is a straight line that [#permalink] ### Show Tags 23 Oct 2015, 01:19 1 This post received KUDOS 1 This post was BOOKMARKED 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. [Reveal] Spoiler: 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. Answer A. _________________ Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS! PS Please send me PM if I do not respond to your question within 24 hours. Board of Directors Joined: 17 Jul 2014 Posts: 2743 Location: United States (IL) Concentration: Finance, Economics GMAT 1: 650 Q49 V30 GPA: 3.92 WE: General Management (Transportation) Re: The graph of which of the following equations is a straight line that [#permalink] ### Show Tags 06 Nov 2015, 22:22 1 This post received KUDOS 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. SVP Joined: 08 Jul 2010 Posts: 2068 Location: India GMAT: INSIGHT WE: Education (Education) The graph of which of the following equations is a straight line that [#permalink] ### Show Tags 07 Nov 2015, 03:16 1 This post received KUDOS Expert's post 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. [Reveal] 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 _________________ Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html 22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION Intern Joined: 05 Nov 2015 Posts: 4 The graph of which of the following equations is a straight line that [#permalink] ### Show Tags 07 Nov 2015, 08:20 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. Answer is A Math Expert Joined: 02 Aug 2009 Posts: 5777 Re: The graph of which of the following equations is a straight line that [#permalink] ### Show Tags 07 Nov 2015, 08:31 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. [Reveal] 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.. _________________ Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html GMAT online Tutor Current Student Joined: 20 Mar 2014 Posts: 2646 Concentration: Finance, Strategy Schools: Kellogg '18 (M) GMAT 1: 750 Q49 V44 GPA: 3.7 WE: Engineering (Aerospace and Defense) Re: The graph of which of the following equations is a straight line that [#permalink] ### Show Tags 07 Nov 2015, 08:38 1 This post received KUDOS 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. [Reveal] 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.. 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 Joined: 02 Aug 2009 Posts: 5777 Re: The graph of which of the following equations is a straight line that [#permalink] ### Show Tags 07 Nov 2015, 09:15 1 This post received KUDOS Expert's post 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.. _________________ Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html GMAT online Tutor Manager Joined: 13 Feb 2011 Posts: 95 The graph of which of the following equations is a straight line that [#permalink] ### Show Tags 13 Feb 2016, 19:33 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. Intern Joined: 10 Aug 2015 Posts: 33 Location: India GMAT 1: 700 Q48 V38 GPA: 3.5 WE: Consulting (Computer Software) Re: The graph of which of the following equations is a straight line that [#permalink] ### Show Tags 11 May 2016, 02:22 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. [Reveal] Spoiler: 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. Answer is A Remember in PS there is only one unique solution to the problem. Director Status: Professional GMAT Tutor Affiliations: AB, cum laude, Harvard University (Class of '02) Joined: 10 Jul 2015 Posts: 604 Location: United States (CA) Age: 38 GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42 GRE 1: 337 Q168 V169 WE: Education (Education) Re: The graph of which of the following equations is a straight line that [#permalink] ### Show Tags 25 May 2016, 22:16 1 This post received KUDOS Attached is a visual that should help. Attachments Screen Shot 2016-05-25 at 9.43.21 PM.png [ 61.25 KiB | Viewed 14662 times ] _________________ Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching, both in-person (San Diego, CA, USA) and online worldwide, since 2002. One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong). You can download my official test-taker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y8zh6qby Date of Birth: 09 December 1979. GMAT Action Plan - McElroy Tutoring Manager Joined: 23 Jun 2009 Posts: 197 Location: Brazil 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] ### Show Tags 10 Sep 2016, 17:17 1 This post received KUDOS Here is an algebraic approach Attachments Screenshot_20160910-211534.jpg [ 551.22 KiB | Viewed 13228 times ] e-GMAT Representative Joined: 04 Jan 2015 Posts: 1029 The graph of which of the following equations is a straight line that [#permalink] ### Show Tags 30 Dec 2016, 23:09 Expert's post 1 This post was BOOKMARKED 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, Saquib Quant Expert e-GMAT To practise ten 700+ Level Number Properties Questions attempt the The E-GMAT Number Properties Knockout _________________ | '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com Senior Manager Joined: 19 Apr 2016 Posts: 275 Location: India GMAT 1: 570 Q48 V22 GMAT 2: 640 Q49 V28 GPA: 3.5 WE: Web Development (Computer Software) Re: The graph of which of the following equations is a straight line that [#permalink] ### Show Tags 23 Jan 2017, 03:51 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. [Reveal] Spoiler: 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. Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 2464 Location: United States (CA) Re: The graph of which of the following equations is a straight line that [#permalink] ### Show Tags 25 Jan 2017, 10:15 Expert's post 1 This post was BOOKMARKED 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. Answer: A _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Intern Joined: 07 Nov 2016 Posts: 8 Location: India GMAT 1: 620 Q47 V29 GPA: 3.9 Re: The graph of which of the following equations is a straight line that [#permalink] ### Show Tags 01 Mar 2017, 19:38 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 Wharton Thread Master Joined: 30 May 2015 Posts: 40 Re: The graph of which of the following equations is a straight line that [#permalink] ### Show Tags 18 May 2017, 22:28 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 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8025 Location: Pune, India Re: The graph of which of the following equations is a straight line that [#permalink] ### Show Tags 18 May 2017, 23:25 Check this post for more on the concept of slope: https://www.veritasprep.com/blog/2016/0 ... line-gmat/ _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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