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# In the x-y plane, both line L and K pass through point (3, 3

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In the x-y plane, both line L and K pass through point (3, 3 [#permalink]  28 Aug 2013, 09:20
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In the x-y plane, both line L and K pass through point (3, 3). Is the y-intercept of line K greater than the y-intercept of line L?

(1) Slope of line L is positive
(2) Slope of line K is less than slope of Line L

According to me the answer should be
[Reveal] Spoiler:
E
but I am not very sure.Sorry I dont have the answer.

Last edited by Bunuel on 28 Aug 2013, 09:37, edited 1 time in total.
RENAMED THE TOPIC.
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Re: Coordinate Geomatry..Plz help [#permalink]  28 Aug 2013, 09:23
nroy347 wrote:
In the x-y plane , both line L and K pass through point (3,3).Is the Y intercept of line K greater than the y intercept of line L?

1.Slope of line L is positive
2.Slope of line K is less than the slope of Line L

According to me the answer should be
[Reveal] Spoiler:
E
but I am not very sure.Sorry I dont have the answer.

You are correct that the answer is E.
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Re: In the x-y plane, both line L and K pass through point (3, 3 [#permalink]  28 Aug 2013, 11:36
I think the answer should be C - as if the like L has the positive slope and the line k has the slope less than slope of the line L - than in that case Line K will always intersect the Y axis above Line L - Keeping in mind they both have to intersect on point (3,3).

Correct me if I am missing on something.

Nikhil
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Re: In the x-y plane, both line L and K pass through point (3, 3 [#permalink]  28 Aug 2013, 17:03
nikhilsehgal wrote:
I think the answer should be C - as if the like L has the positive slope and the line k has the slope less than slope of the line L - than in that case Line K will always intersect the Y axis above Line L - Keeping in mind they both have to intersect on point (3,3).

Correct me if I am missing on something.

Nikhil

nikhil,

Even I think so. But we might be wrong.
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Re: Coordinate Geomatry..Plz help [#permalink]  28 Aug 2013, 17:41
1
KUDOS
fameatop wrote:
nroy347 wrote:
In the x-y plane , both line L and K pass through point (3,3).Is the Y intercept of line K greater than the y intercept of line L?

1.Slope of line L is positive
2.Slope of line K is less than the slope of Line L

According to me the answer should be
[Reveal] Spoiler:
E
but I am not very sure.Sorry I dont have the answer.

You are correct that the answer is E.

IMO B

line L:
$$Y = MX+C$$

line k:
$$Y = NX + D$$

both are passing from $$(3,3)$$
therefore :
$$3M+C=3N+D$$
$$3(M-N) = D-C$$

now statement 2 :
$$M>N$$
THREFORE
$$D-C > 0$$

hence SUFFICIENT
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Re: In the x-y plane, both line L and K pass through point (3, 3 [#permalink]  28 Aug 2013, 18:43
nroy347 wrote:
In the x-y plane, both line L and K pass through point (3, 3). Is the y-intercept of line K greater than the y-intercept of line L?

(1) Slope of line L is positive
(2) Slope of line K is less than slope of Line L

According to me the answer should be
[Reveal] Spoiler:
E
but I am not very sure.Sorry I dont have the answer.

Hi,

I too got B as answer.

Consider the line L
Y=mx+b

For line K
y=nx+c

Both the line passes through Point (3,3)
hence
3m+b=3n+c
3(m-n)=c-b

is c>b?
1) Slope of line L is positive does not give any details of n so insufficent
2) m<n
m-n<0 => apply this in question
so o>c-b
c>b
Statement 2 is sufficient
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Re: In the x-y plane, both line L and K pass through point (3, 3 [#permalink]  28 Aug 2013, 19:08
nikhilsehgal wrote:
I think the answer should be C - as if the like L has the positive slope and the line k has the slope less than slope of the line L - than in that case Line K will always intersect the Y axis above Line L - Keeping in mind they both have to intersect on point (3,3).

Correct me if I am missing on something.

Nikhil

nikhil,

Even I think so. But we might be wrong.

Folks - Line K has slope less than line C's Slope. What if slope of K is negative ?? In that case, Y intercept may or may not be greater. Hence both the conditin together is not sufficient. Hence IMO it has to be E.
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Re: In the x-y plane, both line L and K pass through point (3, 3 [#permalink]  28 Aug 2013, 22:20
I would like to solve it by the understanding the relative position of line in the plane.

+ve slope means line is making an angle < 90 degree with X-axis on the left hand side. Greater the slope greater the angle, while keeping the angle < 90 with x - axis on left hand side. With 90 degree angle with x axis , slope become undefined.
thus, greater the angle, lower the value of Y intercept. Keep in mind both the lines pass through the same point (3,3)

Stmt 1: Slope of line L is positive
This does not say anything about the slope of like k.
1. Slope of line K could be +ve , but less than that of line L, thus in this case, y intercept of line K would be higher.
2. If slope of line K > slope of line L, then y intercept of line K would be lower.
Thus,Insufficient.

(2) Slope of line K is less than slope of Line L
This is point 2 mentioned under choice 1 above. Thus, we can say that y intercept of line K would be higher.
Thus, Sufficient.

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Re: In the x-y plane, both line L and K pass through point (3, 3 [#permalink]  29 Aug 2013, 01:46
If they have different slopes (inclination), then they must have different y interceptors (where they intercept the y axis)

I think B is sufficient.
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Re: In the x-y plane, both line L and K pass through point (3, 3 [#permalink]  29 Aug 2013, 01:56
What if L has negative slope and K has positive slope.In above we have taken both L and K as positive slope.The answer will not change??
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Re: In the x-y plane, both line L and K pass through point (3, 3 [#permalink]  29 Aug 2013, 02:00
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nroy347 wrote:
What if L has negative slope and K has positive slope.In above we have taken both L and K as positive slope.The answer will not change??

since statement 2 says that slope of K is less than slope of L...

In that case If slope of L is negative ..then slope of K cannot be positive..(since slope K < slope L)

HOPE it helps
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Re: In the x-y plane, both line L and K pass through point (3, 3   [#permalink] 29 Aug 2013, 02:00
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