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In the xy-coordinate system, do any points on line k lie in quadrant I

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In the xy-coordinate system, do any points on line k lie in quadrant I [#permalink] New post   15 Feb 2012, 17:10
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In the xy-coordinate system, do any points on line k lie in quadrant III?

(1) Line k has y-intercept 2

(2) Line k has slope 2/3
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Re: In the xy-coordinate system, do any points on line k lie in quadrant I [#permalink] New post   15 Feb 2012, 17:34
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In the xy-coordinate system, do any points on line k lie in quadrant III?

You should just visualize this to solve.

(1) Line k has y-intercept 2 --> if the slope is negative or zero then K will not pass through the III quadrant but if it's positive then it will. Not sufficient.

(2) Line k has slope 2/3 --> any line with positive slope passes through the quadrants I and III. Sufficient.

Answer: B.

Check the image below:



Red and blue lines do not pass through III quadrant and green one does. Notice that any line parallel to green line (so with a slope of 2/3) will also pass through III quadrant.

Some notes:
1. If the slope of line is negative, line WILL intersect quadrants II and IV. X and Y intersects of the line with negative slope have the same sign. Therefore if X and Y intersects are positive, line intersects the quadrant I too, if negative quadrant III.

2. If the slope of line is positive, line WILL intersect quadrants I and III. Y and X intersects of the line with positive slope have opposite signs. Therefore if X intersect is negative, line intersects the quadrant II too, if positive quadrant IV.

3. Every line (but the one crosses origin OR parallel to X or Y axis OR X and Y axis themselves) crosses three quadrants. Only the line which crosses origin (0,0) OR is parallel of either of axis crosses two quadrants.

4. If a line is horizontal the line has slope 0, is parallel to X-axis and crosses quadrant I and II, if the Y intersect is positive OR quadrants III and IV, if the Y intersect is negative. Equation of such line is y=b, where b is y intersect.

5. If a line is vertical, the slope is not defined, line is parallel to Y-axis and crosses quadrant I and IV, if the X intersect is positive and quadrant II and III, if the X intersect is negative. Equation of such line is x=a, where a is x-intercept.

Check this: https://gmatclub.com/forum/in-the-xy-coo ... 86074.html and this: https://gmatclub.com/forum/math-coordina ... 87652.html for more.

Hope it helps.

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Re: In the xy-coordinate system, do any points on line k lie in quadrant I [#permalink] New post   15 Jan 2013, 04:48
Great bit of theory, Thanks bunuel!
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Re: In the xy-coordinate system, do any points on line k lie in quadrant I [#permalink] New post   27 Jun 2013, 22:28
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Coordinate Geometry: math-coordinate-geometry-87652.html

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Re: In the xy-coordinate system, do any points on line k lie in quadrant I [#permalink] New post   27 Jun 2013, 23:26
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Dear Bunuel,
I just want to clear my doubt. If the 2nd statement had been " Line K has negative slope" then we would have required both statements together to answer the question. correct??
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Narenn
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Re: In the xy-coordinate system, do any points on line k lie in quadrant I [#permalink] New post   27 Jun 2013, 23:31
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Narenn wrote:
Dear Bunuel,
I just want to clear my doubt. If the 2nd statement had been " Line K has negative slope" then we would have required both statements together to answer the question. correct??
Regards,
Narenn


Absolutely. Notice that in this case the answer to the question would be NO.
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Re: In the xy-coordinate system, do any points on line k lie in quadrant I [#permalink] New post   27 Jun 2013, 23:53
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hmm.. You are correct.
Thanks
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Re: In the xy-coordinate system, do any points on line k lie in quadrant I [#permalink] New post   27 Jun 2013, 23:56
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Narenn wrote:
hmm.. You are correct.
Thanks


Let me make clear: you are correct the answer would be C, but the answer to the question whether "any points on line k lie in quadrant III" would be NO.
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Re: In the xy-coordinate system, do any points on line k lie in quadrant I [#permalink] New post   12 Feb 2019, 22:34
Bunuel wrote:
In the xy-coordinate system, do any points on line k lie in quadrant III?

You should just visualize this to solve.

(1) Line k has y-intercept 2 --> if the slope is negative or zero then K will not pass through the III quadrant but if it's positive then it will. Not sufficient.

(2) Line k has slope 2/3 --> any line with positive slope passes through the quadrants I and III. Sufficient.

Answer: B.

Check the image below:



Red and blue lines do not pass through III quadrant and green one does. Notice that any line parallel to green line (so with a slope of 2/3) will also pass through III quadrant.

Some notes:
1. If the slope of line is negative, line WILL intersect quadrants II and IV. X and Y intersects of the line with negative slope have the same sign. Therefore if X and Y intersects are positive, line intersects the quadrant I too, if negative quadrant III.

2. If the slope of line is positive, line WILL intersect quadrants I and III. Y and X intersects of the line with positive slope have opposite signs. Therefore if X intersect is negative, line intersects the quadrant II too, if positive quadrant IV.

3. Every line (but the one crosses origin OR parallel to X or Y axis OR X and Y axis themselves) crosses three quadrants. Only the line which crosses origin (0,0) OR is parallel of either of axis crosses two quadrants.

4. If a line is horizontal the line has slope 0, is parallel to X-axis and crosses quadrant I and II, if the Y intersect is positive OR quadrants III and IV, if the Y intersect is negative. Equation of such line is y=b, where b is y intersect.

5. If a line is vertical, the slope is not defined, line is parallel to Y-axis and crosses quadrant I and IV, if the X intersect is positive and quadrant II and III, if the X intersect is negative. Equation of such line is x=a, where a is x-intercept.

Check this: https://gmatclub.com/forum/in-the-xy-coo ... 86074.html and this: https://gmatclub.com/forum/math-coordina ... 87652.html for more.

Hope it helps.

Show Spoiler
Attachment:
graph (2).png


I am not clear the below issue. Kindly help me to clear the below issue.

In your graph, you have showed a line , h(x) = 2/3 X+2 , where slope is 2/3.

But if I calculate slope form your figure, it is -2/3.

slope= rise/run = 2/-3=-2/3.
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Re: In the xy-coordinate system, do any points on line k lie in quadrant I [#permalink] New post   12 Feb 2019, 23:26
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Rashed12 wrote:
Bunuel wrote:
In the xy-coordinate system, do any points on line k lie in quadrant III?

You should just visualize this to solve.

(1) Line k has y-intercept 2 --> if the slope is negative or zero then K will not pass through the III quadrant but if it's positive then it will. Not sufficient.

(2) Line k has slope 2/3 --> any line with positive slope passes through the quadrants I and III. Sufficient.

Answer: B.

Check the image below:



Red and blue lines do not pass through III quadrant and green one does. Notice that any line parallel to green line (so with a slope of 2/3) will also pass through III quadrant.

Some notes:
1. If the slope of line is negative, line WILL intersect quadrants II and IV. X and Y intersects of the line with negative slope have the same sign. Therefore if X and Y intersects are positive, line intersects the quadrant I too, if negative quadrant III.

2. If the slope of line is positive, line WILL intersect quadrants I and III. Y and X intersects of the line with positive slope have opposite signs. Therefore if X intersect is negative, line intersects the quadrant II too, if positive quadrant IV.

3. Every line (but the one crosses origin OR parallel to X or Y axis OR X and Y axis themselves) crosses three quadrants. Only the line which crosses origin (0,0) OR is parallel of either of axis crosses two quadrants.

4. If a line is horizontal the line has slope 0, is parallel to X-axis and crosses quadrant I and II, if the Y intersect is positive OR quadrants III and IV, if the Y intersect is negative. Equation of such line is y=b, where b is y intersect.

5. If a line is vertical, the slope is not defined, line is parallel to Y-axis and crosses quadrant I and IV, if the X intersect is positive and quadrant II and III, if the X intersect is negative. Equation of such line is x=a, where a is x-intercept.

Check this: https://gmatclub.com/forum/in-the-xy-coo ... 86074.html and this: https://gmatclub.com/forum/math-coordina ... 87652.html for more.

Hope it helps.

Show Spoiler
Attachment:
graph (2).png


I am not clear the below issue. Kindly help me to clear the below issue.

In your graph, you have showed a line , h(x) = 2/3 X+2 , where slope is 2/3.

But if I calculate slope form your figure, it is -2/3.

slope= rise/run = 2/-3=-2/3.


How did you calculate the slope?

Given two points \((x_1,y_1)\) and \((x_2,y_2)\) on a line, the slope \(m\) of the line is:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

So, take tow points on green line, say (-3, 0) and (0, 2). The slope of a line passing those points is \(m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-0}{0-(-3)}=\frac{2}{3}\)

Also, if the equation of the line is given in the Point-intercept form: \(y=mx+b\), then \(m\) is the slope. So, the slope of h(x) = 2/3*x + 2 is 2/3.

P.S. Please do NOT report a post the way you did. Reporting should generally be used only if the post breaks forum rules. NOT if you need some help. Use reply for that.
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Re: In the xy-coordinate system, do any points on line k lie in quadrant I [#permalink] New post   16 May 2019, 03:37
Who said that line k is infinitive? i.e. could start and end in quadrant I

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Re: In the xy-coordinate system, do any points on line k lie in quadrant I [#permalink] New post   16 May 2019, 03:54
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Duco11000 wrote:
Who said that line k is infinitive? i.e. could start and end in quadrant I

Posted from my mobile device


In Geometry a line:
• is straight (no bends),
• has no thickness, and.
• extends in both directions without end (infinitely).
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In the xy-coordinate system, do any points on line k lie in quadrant 3 [#permalink] New post   26 Jun 2021, 16:10
In the xy-coordinate system, do any points on line k lie in quadrant III? This is a Data sufficiency question so the answers are generic

(1) Line k has y-intercept 2

(2) Line k has slope 2/3
​
I have a doubt here, I know that the answer is B, but I have a doubt. Cant a line with a positive slop start from a y intercept in the 1st quadrant or cant it pass through 4th and 1st quadrant or 2nd a 1st quadrant. Here it is only mentioned line K. it can start from anywhere but then why if it has a positive slope it has to go through 3rd quadrant. Does the principle of extension of a line to infinity apply here too. I thought when a line K is given its assumed to be finite in a coordinate geometry question.
​
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Re: In the xy-coordinate system, do any points on line k lie in quadrant 3 [#permalink] New post   26 Jun 2021, 16:28
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arry232 wrote:
I thought when a line K is given its assumed to be finite in a coordinate geometry question.
​


It's the opposite, in fact. In coordinate geometry, a line is infinite. If a question means to talk about a finite length, it will usually talk about a "line segment", or provide a diagram that illustrates just a line segment (or edge of a square, etc). It's because coordinate geometry lines are infinite that the answer here is B. If the line here was instead a line segment, so was finite, then the answer would be E, as your examples prove.
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Re: In the xy-coordinate system, do any points on line k lie in quadrant I [#permalink] New post   28 Mar 2023, 04:14
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Re: In the xy-coordinate system, do any points on line k lie in quadrant I [#permalink]
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