Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 25 Aug 2016, 03:34

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In the coordinate system above, which of the following is

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 178
Followers: 4

Kudos [?]: 1870 [5] , given: 0

In the coordinate system above, which of the following is [#permalink]

### Show Tags

27 Dec 2012, 07:38
5
KUDOS
7
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

71% (02:11) correct 29% (01:14) wrong based on 962 sessions

### HideShow timer Statistics

Attachment:

Line L.png [ 6.88 KiB | Viewed 12045 times ]
In the coordinate system above, which of the following is the equation of line l ?

(A) 2x - 3y = 6
(B) 2x + 3y = 6
(C) 3x + 2y = 6
(D) 2x - 3y = -6
(E) 3x - 2y = -6
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 34432
Followers: 6254

Kudos [?]: 79439 [1] , given: 10016

Re: In the coordinate system above, which of the following is [#permalink]

### Show Tags

27 Dec 2012, 07:45
1
KUDOS
Expert's post
4
This post was
BOOKMARKED

In the coordinate system above, which of the following is the equation of line l ?

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

Notice that line l passes through points (3,0) and (0,2), so its slope is $$m=\frac{y_2-y_1}{x_2-x_1}=-\frac{2}{3}$$ (given two points $$(x_1,y_1)$$ and $$(x_2,y_2)$$ on a line, the slope $$m$$ of the line is $$m=\frac{y_2-y_1}{x_2-x_1}$$).

Only option B, when written in $$y=mx+b$$ form has the slope of -2/3.

_________________
Current Student
Joined: 27 Jan 2013
Posts: 71
Location: India
Concentration: General Management, Operations
GMAT 1: 740 Q50 V40
GPA: 3.51
WE: Other (Transportation)
Followers: 3

Kudos [?]: 3 [3] , given: 34

Re: In the coordinate system above, which of the following is [#permalink]

### Show Tags

13 Apr 2013, 00:21
3
KUDOS
Bunuel wrote:

In the coordinate system above, which of the following is the equation of line l ?

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

Notice that line l passes through points (3,0) and (0,2), so its slope is $$m=\frac{y_2-y_1}{x_2-x_1}=-\frac{2}{3}$$ (given two points $$(x_1,y_1)$$ and $$(x_2,y_2)$$ on a line, the slope $$m$$ of the line is $$m=\frac{y_2-y_1}{x_2-x_1}$$).

Only option B, when written in $$y=mx+b$$ form has the slope of -2/3.

Hi Bunnel...A small query
Can we assume (As u have done in your solution) that the line passes through points (3,0) and (0,2). I mean can we safely interpret graphs on the GMAT??Since it is not explicitly stated that the line passes through those two specific points.
My approach to the above problem was as follows.
What we know from the graph is this
x and y co-ordinates of line l are both positive, x co-ordinate is > 2 and y co-ordinate is > 1
A, D and E are clearly out since x and y co-ordinates will have opposite signs
putting y=0 in choice C x=2 - Incorrect (as x co-ordinate > 2)
Only B left
Cheers
Math Expert
Joined: 02 Sep 2009
Posts: 34432
Followers: 6254

Kudos [?]: 79439 [0], given: 10016

Re: In the coordinate system above, which of the following is [#permalink]

### Show Tags

13 Apr 2013, 03:56
Expert's post
1
This post was
BOOKMARKED
Dipankar6435 wrote:
Bunuel wrote:

In the coordinate system above, which of the following is the equation of line l ?

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

Notice that line l passes through points (3,0) and (0,2), so its slope is $$m=\frac{y_2-y_1}{x_2-x_1}=-\frac{2}{3}$$ (given two points $$(x_1,y_1)$$ and $$(x_2,y_2)$$ on a line, the slope $$m$$ of the line is $$m=\frac{y_2-y_1}{x_2-x_1}$$).

Only option B, when written in $$y=mx+b$$ form has the slope of -2/3.

Hi Bunnel...A small query
Can we assume (As u have done in your solution) that the line passes through points (3,0) and (0,2). I mean can we safely interpret graphs on the GMAT??Since it is not explicitly stated that the line passes through those two specific points.
My approach to the above problem was as follows.
What we know from the graph is this
x and y co-ordinates of line l are both positive, x co-ordinate is > 2 and y co-ordinate is > 1
A, D and E are clearly out since x and y co-ordinates will have opposite signs
putting y=0 in choice C x=2 - Incorrect (as x co-ordinate > 2)
Only B left
Cheers

OG13 solution makes the same exact assumption "The line is shown going through the points (0,2) and (3,0)..."
_________________
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 630
Followers: 76

Kudos [?]: 1005 [1] , given: 136

Re: In the coordinate system above, which of the following is [#permalink]

### Show Tags

15 Apr 2013, 07:30
1
KUDOS
2
This post was
BOOKMARKED
Attachment:
Line L.png
In the coordinate system above, which of the following is the equation of line l ?

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

From the given figure, we can see that the line has positive intercept on both the x and y axis. Thus we can eliminate all the options except B and C. Now the intercept on the x-axis is more than 2. For option C, the x-intercept comes as 2, thus the answer has to be B.
_________________
Intern
Joined: 03 Nov 2013
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 5

Re: In the coordinate system above, which of the following is [#permalink]

### Show Tags

07 Nov 2013, 23:41
Just a different way of approaching the problem...
since we know the y-intercept is -c/b when the equation is given in the form ax+by +c =0.. simply use what's on the right side of the equation (it'll turn negative when moved to the left) and divide by b.
Intern
Joined: 10 Nov 2013
Posts: 20
Location: United States
Concentration: Healthcare, Strategy
WE: Information Technology (Health Care)
Followers: 1

Kudos [?]: 10 [0], given: 130

Re: In the coordinate system above, which of the following is [#permalink]

### Show Tags

01 Dec 2013, 11:59
Bunuel wrote:
Dipankar6435 wrote:
Bunuel wrote:

In the coordinate system above, which of the following is the equation of line l ?

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

Notice that line l passes through points (3,0) and (0,2), so its slope is $$m=\frac{y_2-y_1}{x_2-x_1}=-\frac{2}{3}$$ (given two points $$(x_1,y_1)$$ and $$(x_2,y_2)$$ on a line, the slope $$m$$ of the line is $$m=\frac{y_2-y_1}{x_2-x_1}$$).

Only option B, when written in $$y=mx+b$$ form has the slope of -2/3.

Hi Bunnel...A small query
Can we assume (As u have done in your solution) that the line passes through points (3,0) and (0,2). I mean can we safely interpret graphs on the GMAT??Since it is not explicitly stated that the line passes through those two specific points.
My approach to the above problem was as follows.
What we know from the graph is this
x and y co-ordinates of line l are both positive, x co-ordinate is > 2 and y co-ordinate is > 1
A, D and E are clearly out since x and y co-ordinates will have opposite signs
putting y=0 in choice C x=2 - Incorrect (as x co-ordinate > 2)
Only B left
Cheers

OG13 solution makes the same exact assumption "The line is shown going through the points (0,2) and (3,0)..."

I agree with Dipankar6435 approach. I used the similar approach since it is not explicitly mentioned that the line passes through and also there is no line markers at the points where the line touches both x and y axis. Since there is a line marker on the x axis that clearly indicates that the x value should be greater than 2, out of the 2 answer choices, I picked B as the right one. Thanks.
Senior Manager
Joined: 28 Apr 2014
Posts: 291
Followers: 1

Kudos [?]: 32 [0], given: 46

Re: In the coordinate system above, which of the following is [#permalink]

### Show Tags

15 May 2014, 10:35
Bunuel wrote:
Dipankar6435 wrote:
Bunuel wrote:

In the coordinate system above, which of the following is the equation of line l ?

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

Notice that line l passes through points (3,0) and (0,2), so its slope is $$m=\frac{y_2-y_1}{x_2-x_1}=-\frac{2}{3}$$ (given two points $$(x_1,y_1)$$ and $$(x_2,y_2)$$ on a line, the slope $$m$$ of the line is $$m=\frac{y_2-y_1}{x_2-x_1}$$).

Only option B, when written in $$y=mx+b$$ form has the slope of -2/3.

Hi Bunnel...A small query
Can we assume (As u have done in your solution) that the line passes through points (3,0) and (0,2). I mean can we safely interpret graphs on the GMAT??Since it is not explicitly stated that the line passes through those two specific points.
My approach to the above problem was as follows.
What we know from the graph is this
x and y co-ordinates of line l are both positive, x co-ordinate is > 2 and y co-ordinate is > 1
A, D and E are clearly out since x and y co-ordinates will have opposite signs
putting y=0 in choice C x=2 - Incorrect (as x co-ordinate > 2)
Only B left
Cheers

OG13 solution makes the same exact assumption "The line is shown going through the points (0,2) and (3,0)..."

Very very strange because in Maths , one is groomed to never make assumptions based on diagrams unless explicitly mentioned .
Intern
Joined: 17 May 2014
Posts: 40
Followers: 0

Kudos [?]: 25 [0], given: 3

Re: In the coordinate system above, which of the following is [#permalink]

### Show Tags

17 May 2014, 06:11
There is another general form of line in co-ordinate plane which is:

x/a + y/b = 1

where a is the point of intersection of line and x-axis and b is the point of intersection of line with y-axis.
Here a=3, b=2
Therefore,

x/3 + y/2 = 1

or

2x + 3y = 6

This solution is valid, if we assume the values of a, and b.

But even if we don’t assume these values, we can eliminate option A), D), and E) because, we can see that both the x intercept and y intercept are positive.

Now, we see a>b through observation, which means coefficient of x is greater than coefficient of y, which is in option B) only. Hence B is the answer.
Intern
Joined: 14 May 2014
Posts: 45
Followers: 0

Kudos [?]: 39 [0], given: 1

Re: In the coordinate system above, which of the following is [#permalink]

### Show Tags

21 May 2014, 04:59
If intercept on the x axis and y axis is known, intercept formula for line is the fastest method to get the equation of the line.

Equation of a line which cut an intercept a at x axis and b at y axis is given by

(x/a) + (y/b) = 1

However, a more useful form of this equation is

bx + ay = ab

using this, equation of line can be found easily by inspection only
Here , Intercept at x axis = a = 3
Intercept at y axis = b = 2
hence, equation of line by putting values
2x+3y =6 hence answer is B
_________________

Help me with Kudos if it helped you "

Mathematics is a thought process.

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 11046
Followers: 510

Kudos [?]: 134 [0], given: 0

Re: In the coordinate system above, which of the following is [#permalink]

### Show Tags

09 Jul 2015, 11:42
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Intern
Joined: 24 Aug 2015
Posts: 10
Followers: 0

Kudos [?]: 1 [1] , given: 0

Re: In the coordinate system above, which of the following is [#permalink]

### Show Tags

07 Oct 2015, 15:37
1
KUDOS
L = (0,2)
X = (3,0)

slope = 2-0/0-3 = -2/3

y = mx + b
y = -2/3x + b

Find b:

2=0+b
b = 2

y=-2/3x + 2
x 3 to eliminated -2/3

3y = -2x +6
3y + 2x = 6
Intern
Status: Current Student
Joined: 27 Mar 2014
Posts: 14
Followers: 0

Kudos [?]: 13 [1] , given: 8

In the coordinate system above, which of the following is [#permalink]

### Show Tags

20 Dec 2015, 05:27
1
KUDOS

Quote:
In the coordinate system above, which of the following is the equation of line l ?

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

Without any calculation Approach!
We know from the graph that X-intercept must be greater than 2.
So, co-efficient of x must be 2. Hence C and E are out.
The equation of straight line is y=mx+b and In the figure we can see that slope must be negative.
Therefore, A and D are out since they have positive slope.
Manager
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 190
Followers: 8

Kudos [?]: 38 [0], given: 2

Re: In the coordinate system above, which of the following is [#permalink]

### Show Tags

13 Jul 2016, 07:51
Attachment:
Line L.png
In the coordinate system above, which of the following is the equation of line l ?

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

We start by defining the equation of line l using the slope-intercept form of a line (y = mx + b), where m = slope and b = the y-intercept.

Notice that line l has two points: (0,2) and (3,0). We can use these two points to determine the slope. The formula for slope is:

m = (change in y)/(change in x) or

m = (y_2 – y_1)/(x_2 – x_1)

Plugging in our points we have:

m = (0 – 2)/(3 – 0)

m = -2/3

We also see from the diagram that the y-intercept of line l is 2. Substituting the slope and the y-intercept into the line equation we have:

y = (-2/3)x + 2

The final step is to recognize that the answer choices are in a different form than is our equation for line l. Thus, we have to manipulate our equation such that it will match one of the answer choices. Let's first multiply the entire equation by 3. This gives us:

3y = -2x + 6

Then add 2x to both sides of the equation:

2x + 3y = 6

_________________

Jeffrey Miller
Jeffrey Miller

Director
Joined: 12 Sep 2015
Posts: 543
Followers: 42

Kudos [?]: 380 [1] , given: 12

Re: In the coordinate system above, which of the following is [#permalink]

### Show Tags

21 Jul 2016, 16:06
1
KUDOS
Top Contributor
Attachment:
Line L.png
In the coordinate system above, which of the following is the equation of line l ?

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

We can see that points (0,2) and (3,0) are ON THE LINE. So, their coordinates must SATISFY the equation of the line.

(A) 2x - 3y = 6. 2(0) - 3(2) = -6 ELIMINATE
(B) 2x + 3y = 6. 2(0) + 3(2) = 6 KEEP
(C) 3x + 2y = 6. 3(0) +2(2) = 4 ELIMINATE
(D) 2x - 3y = -6. 2(0) - 3(2) = -6 KEEP
(E) 3x - 2y = -6. 3(0) - 2(2) = -4 ELIMINATE

Great. We're down to B or D

Let's test (3,0).
(B) 2x + 3y = 6. 2(3) + 3(0) = 6 KEEP
(D) 2x - 3y = -6. 2(3) - 3(0) = 6 ELIMINATE

[Reveal] Spoiler:
B

RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

Brent also tutors students for the GMAT

Re: In the coordinate system above, which of the following is   [#permalink] 21 Jul 2016, 16:06
Similar topics Replies Last post
Similar
Topics:
37 In the rectangular coordinate system shown above, which quad 11 03 Mar 2014, 01:21
12 In the rectangular coordinate system above, for which of the 11 22 Nov 2010, 06:29
15 In the rectangular coordinate system above the area of 8 22 Nov 2010, 06:27
12 In a rectangular coordinate system, which of the following 8 20 Oct 2010, 02:55
57 In the rectangular coordinate system shown above, which 14 10 Feb 2010, 13:06
Display posts from previous: Sort by