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In the xy plane line k has a positive slope and and [#permalink]
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In the xy plane line k has a positive slope and and xintercept 4. if the area of the triangle formed by line k and the two axes is 12, what is the y intercept of line k A. 6 B. 4 C. 3 D. 3 E. 6 Answer is 6. can someone explain how i would derive to this ans. I got 6
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Originally posted by cmugeria on 09 Sep 2010, 10:08.
Last edited by Bunuel on 27 Jun 2013, 23:08, edited 3 times in total.
Edited the question



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Re: GMAT PREP QUES PLEASE HELP [#permalink]
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09 Sep 2010, 10:18
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Re: GMAT PREP QUES PLEASE HELP [#permalink]
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09 Sep 2010, 14:17
Positive slope (line goes like /) and positive xintercept means that yintercept will be negative. The area of the triangle would be (1/2)*(value of xintercept)*(the value of yintercept) > > > as yintercept is negative, then .
Answer: A.
Hope it helps.
Thanks Bunuel for the explanation. However i tried graphing this to make sense to me but still buffled....
Does this mean if the slope was negative then the y intercept would have been 6.



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Re: GMAT PREP QUES PLEASE HELP [#permalink]
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09 Sep 2010, 14:40
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Re: GMAT PREP QUES PLEASE HELP [#permalink]
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10 Sep 2010, 10:42
Thanks Bunuel. As usual your answers are easy to understand. You would be an excellent math tutor !



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Re: GMAT PREP QUES PLEASE HELP [#permalink]
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11 Sep 2010, 14:20
Easy one. Only catchy elements were positive slope and intercept. I calculated 6 for the right triangle having 4 as one side and 12 as area. Then intercept was 6 (it will cut y axis below 0)
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Re: GMAT PREP QUES PLEASE HELP [#permalink]
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11 Sep 2010, 20:59
Since the slope of this line is positive... the y intercept will be negative. Hence 6. The graphical method posted above really simplifies things while you're solving a coordinate geometry question. Hope this answers your question.



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Re: GMAT PREP QUES PLEASE HELP [#permalink]
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04 Nov 2010, 15:41
I took 6. But now looking at ur answers I understood about my silly mistake thank you Bunnel....
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Re: Coordinate Geometry [#permalink]
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07 Jun 2012, 00:49
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Area formed by a line with the axes = 1/2.xintercept.yintercept
1/2 . 4 . yintercept = 12
yintercept = 6
As the line has positive slope and cuts the positive xaxis, its yintercept is negative
Hence, yintercept = 6



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Re: Coordinate Geometry [#permalink]
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07 Jun 2012, 02:02
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Val1986 wrote: In the xy plane, line k has a positive slope and xintersept 4. If the area of the triangle formed by line k and the two axes is 12, what is the yintercept of line k?
A. 6 B. 4 C. 3 D. 3 E. 6 Hi, As per the below diagram, the triangle will have xintercept as (4,0) and negative yintercept (since, slope is positive). Area of triangle would be = 1/2*4*y = 12 or y = 6 But since yintercept is negative, it should be equal to 6.
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File comment: Plotting the line.
area.jpg [ 3.74 KiB  Viewed 16139 times ]



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Re: GMAT PREP QUES PLEASE HELP [#permalink]
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07 Jun 2012, 18:33
Bunuel wrote: cmugeria wrote: in the xy plane line k has a positive slope and and xintercept 4. if the area of the triangle formed by line k and the two axes is 12, what is the y intercept of line k
a. 6 b. 4 c. 3 d. 3 e. 6
Answer is 6. can someone explain how i would derive to this ans. I got 6 Positive slope (line goes like /) and positive xintercept means that yintercept will be negative. The area of the triangle would be (1/2)*(value of xintercept)*(the value of yintercept) > \(area=\frac{1}{2}*4*y=12\) > \(y=6\) > as yintercept is negative, then \(y=6\). Answer: A. Hope it helps. Excellent answer. I've always had a minor problem with area of triangles. Of course, the formula for area is .5bh. When can you just take two sides as b & h, and when do you have to do some math to find them?



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Re: In the xy plane line k has a positive slope and and [#permalink]
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27 Jun 2013, 23:46



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Re: In the xy plane line k has a positive slope and and [#permalink]
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28 Jun 2013, 02:08



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Re: In the xy plane line k has a positive slope and and [#permalink]
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02 May 2014, 02:49
There is no hard and fast rule that if slope is positive then Yintercept is negative. If slope is positive then both x and y intercept are positive (what I have observed) So there is confusion why cant we choose 6 as answer here? Pls guide



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Re: In the xy plane line k has a positive slope and and [#permalink]
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02 May 2014, 02:54
hapless12 wrote: There is no hard and fast rule that if slope is positive then Yintercept is negative. If slope is positive then both x and y intercept are positive (what I have observed) So there is confusion why cant we choose 6 as answer here? Pls guide First of all, please do read the solutions above. For example, check here: inthexyplanelinekhasapositiveslopeandand100739.html#p778346 and here: inthexyplanelinekhasapositiveslopeandand100739.html#p778520Theory: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 Xaxis 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 Yaxis 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 xintercept. Theory on Coordinate Geometry: mathcoordinategeometry87652.htmlDS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=41PS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=62
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Re: In the xy plane line k has a positive slope and and [#permalink]
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06 Sep 2014, 12:31
cmugeria wrote: In the xy plane line k has a positive slope and and xintercept 4. if the area of the triangle formed by line k and the two axes is 12, what is the y intercept of line k A. 6 B. 4 C. 3 D. 3 E. 6 Answer is 6. can someone explain how i would derive to this ans. I got 6 positive slope.. both x & y increases.. i.e. falls mostly in 1 & 3 quadrant. given xintercept is 4 then y intercept must be negative hence last two options are cancelled. area = 12 then applying area of the triangle (b*h)/2=> we shall get 6 & since it should fall on y section it should be 6(3rd quadrant , y is ive)



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Re: In the xy plane line k has a positive slope and and [#permalink]
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31 Oct 2016, 17:21
This question may appear to involve setting up the equation of a line, but really you're only applying knowledge of triangles.
Here we go: From the prompt, we know (1) slope of this line is positive (aka upward trending), (2) a xintercept of 4 (which we can plot on the graph), (3) and that the triangle it forms with the axis has an area of 12.
Because of the xintercept being given to us, we know that the base of the triangle is 4. We can solve for the height by using the following equation: 12 = (1/2)(h)(4) > h = 6
Because h is 6 we know that's where the y intercept is and thus E is the correct answer.



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