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In the xy plane line k has a positive slope and and [#permalink]
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 11126 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) _________________
If you like my post, consider giving me some KUDOS !!!!! Like you I need them
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.
Re: Coordinate Geometry [#permalink]
07 Jun 2012, 01:02
1
This post received KUDOS
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.
Re: GMAT PREP QUES PLEASE HELP [#permalink]
07 Jun 2012, 17:33
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?
Re: In the xy plane line k has a positive slope and and [#permalink]
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
Re: In the xy plane line k has a positive slope and and [#permalink]
02 May 2014, 01:54
1
This post received KUDOS
Expert's post
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
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]
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]
29 Sep 2015, 08:07
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