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In the coordinate system above, which of the following is

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In the coordinate system above, which of the following is [#permalink] New post 27 Dec 2012, 06:38
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Attachment:
Line L.png
Line L.png [ 6.88 KiB | Viewed 3765 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
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Re: In the coordinate system above, which of the following is [#permalink] New post 27 Dec 2012, 06:45
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Image
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.

Answer: B.
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Re: In the coordinate system above, which of the following is [#permalink] New post 12 Apr 2013, 23:21
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Bunuel wrote:
Image
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.

Answer: B.


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
Checking answer choices -
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 :)
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Re: In the coordinate system above, which of the following is [#permalink] New post 13 Apr 2013, 02:56
Expert's post
Dipankar6435 wrote:
Bunuel wrote:
Image
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.

Answer: B.


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
Checking answer choices -
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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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: In the coordinate system above, which of the following is [#permalink] New post 15 Apr 2013, 06:30
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Walkabout wrote:
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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Re: In the coordinate system above, which of the following is [#permalink] New post 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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Re: In the coordinate system above, which of the following is [#permalink] New post 01 Dec 2013, 10:59
Bunuel wrote:
Dipankar6435 wrote:
Bunuel wrote:
Image
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.

Answer: B.


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
Checking answer choices -
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.
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Re: In the coordinate system above, which of the following is [#permalink] New post 15 May 2014, 09:35
Bunuel wrote:
Dipankar6435 wrote:
Bunuel wrote:
Image
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.

Answer: B.


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
Checking answer choices -
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 .
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Re: In the coordinate system above, which of the following is [#permalink] New post 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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Re: In the coordinate system above, which of the following is [#permalink] New post 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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