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

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Manager
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In the coordinate system above, which of the following is [#permalink]  27 Dec 2012, 06:38
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Line L.png [ 6.88 KiB | Viewed 4924 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: 25243
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Kudos [?]: 34872 [1] , given: 3995

Re: In the coordinate system above, which of the following is [#permalink]  27 Dec 2012, 06:45
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Expert's post
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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.

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Kudos [?]: 19 [1] , given: 34

Re: In the coordinate system above, which of the following is [#permalink]  12 Apr 2013, 23:21
1
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: 25243
Followers: 3916

Kudos [?]: 34872 [0], given: 3995

Re: In the coordinate system above, which of the following is [#permalink]  13 Apr 2013, 02:56
Expert's post
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)..."
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Kudos [?]: 658 [1] , given: 135

Re: In the coordinate system above, which of the following is [#permalink]  15 Apr 2013, 06:30
1
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Expert's post
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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.
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Intern
Joined: 03 Nov 2013
Posts: 2
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Kudos [?]: 0 [0], given: 5

Re: In the coordinate system above, which of the following is [#permalink]  07 Nov 2013, 22:41
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.
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Joined: 10 Nov 2013
Posts: 17
Location: United States
Concentration: Healthcare, Strategy
Schools: Kellogg PT '15
WE: Information Technology (Health Care)
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Kudos [?]: 7 [0], given: 109

Re: In the coordinate system above, which of the following is [#permalink]  01 Dec 2013, 10:59
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
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Kudos [?]: 26 [0], given: 46

Re: In the coordinate system above, which of the following is [#permalink]  15 May 2014, 09:35
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: 16 May 2014
Posts: 40
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Kudos [?]: 16 [0], given: 3

Re: In the coordinate system above, which of the following is [#permalink]  17 May 2014, 05:11
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.
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Joined: 14 May 2014
Posts: 45
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Kudos [?]: 18 [0], given: 1

Re: In the coordinate system above, which of the following is [#permalink]  21 May 2014, 03:59
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
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Re: In the coordinate system above, which of the following is   [#permalink] 21 May 2014, 03:59
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