In the xy-plane, line k has positive slope and x-intercept 4. If the

Question

In the xy-plane, line k has positive slope 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

Bunuel · Accepted Answer

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.

Bunuel · Answer

Below are two lines with positive slope (blue) and negative slope (red) which both satisfy x-intercept=4 and area=12. graph.php (1).png Hope it helps.

cmugeria · Answer

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.

cmugeria · Answer

Thanks Bunuel. As usual your answers are easy to understand. You would be an excellent math tutor !

gnan · Answer

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

cyberjadugar · Answer

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.

geometric · Answer

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?

hapless12 · Answer

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

Bunuel · Answer

Please check here: https://gmatclub.com/forum/in-the-xy-pla ... ml#p778346 and here: https://gmatclub.com/forum/in-the-xy-pla ... ml#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: https://gmatclub.com/forum/math-coordina ... 87652.html DS Coordinate Geometry Problems to practice: https://gmatclub.com/forum/search.php?se ... &tag_id=41 PS Coordinate Geometry Problems to practice: https://gmatclub.com/forum/search.php?se ... &tag_id=62

EgmatQuantExpert · Answer

Solution

Given
  
 • In the xy plane line k has a positive slope.
• x- intercept of line k is 4.
• Area of the triangle formed by line k and the two axes is 12

To find  
 • y intercept of line k.

Approach  
 • Area of the triangle formed by line k and two axes = 1 /2 * x intercept * y intercept = 12
• ½ * 4 * y intercept = 12
• y intercept = 6

However, area formula uses the length and it is always positive.
But, if the slope of line k is positive then y intercept will be negative.
 • Thus, y-intercept = -6

Hence, the correct answer is option A.

hemantdixit9 · Answer

Yes, that is correct.

bumpbot · Answer

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