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Intern  Joined: 22 Dec 2009
Posts: 20
In the xy plane line k has a positive slope and and  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 68% (01:18) correct 32% (01:24) wrong based on 1188 sessions

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In the xy plane line k has a positive slope and and x-intercept 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

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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Math Expert V
Joined: 02 Sep 2009
Posts: 55271
Re: GMAT PREP QUES PLEASE HELP  [#permalink]

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10
6
cmugeria wrote:
in the xy plane line k has a positive slope and and x-intercept 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 x-intercept means that y-intercept will be negative. The area of the triangle would be (1/2)*(value of x-intercept)*(the value of y-intercept) --> $$area=\frac{1}{2}*4*|y|=12$$ --> $$|y|=6$$ --> as y-intercept is negative, then $$y=-6$$.

Answer: A.

Hope it helps.
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Intern  Joined: 22 Dec 2009
Posts: 20
Re: GMAT PREP QUES PLEASE HELP  [#permalink]

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Positive slope (line goes like /) and positive x-intercept means that y-intercept will be negative. The area of the triangle would be (1/2)*(value of x-intercept)*(the value of y-intercept) --> --> --> as y-intercept 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.
Math Expert V
Joined: 02 Sep 2009
Posts: 55271
Re: GMAT PREP QUES PLEASE HELP  [#permalink]

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cmugeria wrote:
Positive slope (line goes like /) and positive x-intercept means that y-intercept will be negative. The area of the triangle would be (1/2)*(value of x-intercept)*(the value of y-intercept) --> --> --> as y-intercept 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.

Below are two lines with positive slope (blue) and negative slope (red) which both satisfy x-intercept=4 and area=12.
Attachment: graph.php (1).png [ 8.7 KiB | Viewed 21658 times ]

Hope it helps.
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Re: GMAT PREP QUES PLEASE HELP  [#permalink]

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Thanks Bunuel. As usual your answers are easy to understand. You would be an excellent math tutor !
Manager  Joined: 20 Jul 2010
Posts: 208
Re: GMAT PREP QUES PLEASE HELP  [#permalink]

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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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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.
Manager  Joined: 23 Sep 2009
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Re: GMAT PREP QUES PLEASE HELP  [#permalink]

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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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1
Area formed by a line with the axes = 1/2.|x-intercept|.|y-intercept|

1/2 . 4 . |y-intercept| = 12

|y-intercept| = 6

As the line has positive slope and cuts the positive x-axis, its y-intercept is negative

Hence, y-intercept = -6
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GMAT 1: 640 Q50 V26 GMAT 2: 660 Q50 V28 GMAT 3: 730 Q50 V38 Re: Coordinate Geometry  [#permalink]

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Val1986 wrote:
In the xy plane, line k has a positive slope and x-intersept 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

Hi,

As per the below diagram, the triangle will have x-intercept as (4,0)
and negative y-intercept (since, slope is positive).

Area of triangle would be = 1/2*4*y = 12
or y = 6
But since y-intercept is negative, it should be equal to -6.
Attachments

File comment: Plotting the line. area.jpg [ 3.74 KiB | Viewed 20143 times ]

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Re: GMAT PREP QUES PLEASE HELP  [#permalink]

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Bunuel wrote:
cmugeria wrote:
in the xy plane line k has a positive slope and and x-intercept 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 x-intercept means that y-intercept will be negative. The area of the triangle would be (1/2)*(value of x-intercept)*(the value of y-intercept) --> $$area=\frac{1}{2}*4*|y|=12$$ --> $$|y|=6$$ --> as y-intercept 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?
Math Expert V
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Re: In the xy plane line k has a positive slope and and  [#permalink]

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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

All DS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=41
All PS 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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Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: In the xy plane line k has a positive slope and and  [#permalink]

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There is no hard and fast rule that if slope is positive then Y-intercept 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
Math Expert V
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Posts: 55271
Re: In the xy plane line k has a positive slope and and  [#permalink]

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1
hapless12 wrote:
There is no hard and fast rule that if slope is positive then Y-intercept 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: in-the-xy-plane-line-k-has-a-positive-slope-and-and-100739.html#p778346 and here: in-the-xy-plane-line-k-has-a-positive-slope-and-and-100739.html#p778520

Theory:
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.

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

DS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=41
PS 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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cmugeria wrote:
In the xy plane line k has a positive slope and and x-intercept 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 x-intercept 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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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 x-intercept 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 x-intercept 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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Re: In the xy plane line k has a positive slope and and  [#permalink]

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