Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

09 Sep 2010, 09:08

15

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

62% (01:48) correct
38% (00:51) wrong based on 716 sessions

HideShow timer Statistics

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 13865 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.

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]

Show Tags

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]

Show Tags

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]

Show Tags

29 Sep 2015, 08:07

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

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

Show Tags

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
[#permalink]
31 Oct 2016, 16:21

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Since my last post, I’ve got the interview decisions for the other two business schools I applied to: Denied by Wharton and Invited to Interview with Stanford. It all...

Marketing is one of those functions, that if done successfully, requires a little bit of everything. In other words, it is highly cross-functional and requires a lot of different...