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

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09 Sep 2010, 09:08

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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

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 \(y=-6\).

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.

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 14493 times ]

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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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.

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.

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?

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

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02 May 2014, 01:49

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

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

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.

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

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06 Sep 2014, 11:31

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

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)

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

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29 Sep 2015, 08:07

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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, 16:21

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 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.

gmatclubot

Re: In the xy plane line k has a positive slope and and
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31 Oct 2016, 16:21

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