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Current Student B
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In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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In the xy-plane, lines k and l intersect at the point (1,1). Is the y-intercept of k greater than the y-intercept of l?

(1) The slope of k is less than the slope of l.
(2) The slope of l is positive.
Math Expert V
Joined: 02 Aug 2009
Posts: 7437
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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6
10
nalinnair wrote:
In the $$xy$$-plane, lines $$k$$ and $$l$$ intersect at the point $$(1,1)$$. Is the $$y$$-intercept of $$k$$ greater than the $$y$$-intercept of $$l$$?

(1) The slope of $$k$$ is less than the slope of $$l$$.
(2) The slope of $$l$$ is positive.

Hi,

An easy question if you are aware of the slopes....

slope is the Increase in Y/ Increase in X.......... OR Vertical increase / Horizontal increase..

If BOTH increase with increase in each other, the SLOPE is Positive... But if Y decreases with increase in X, slope is -ive....
so for a point (1,1), a line intercepting above Y as 1, it is -ive and with increase in Y, the slope will have even lesser value...
At y=1, slope is 0 and at y<1, the slopw will keep increasing as the value of Y increases...

So the relation of y-intercept is dependent on slope.. lesser the slope higher is the intercept..

(1) The slope of $$k$$ is less than the slope of $$l$$.
As seen above y intercept of line l will be more than line k...
Suff

(2) The slope of $$l$$ is positive.
we require to know slope of line k also
Insuff

A
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Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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26
1
7
We can write the equation of the line in slope-intercept form as follow: [Where M is the slope and C is the y-intercept]

For Line K : Yk = Mk.Xk +Ck
For Line L : Yl = Ml.Xl + Cl

Now, since these lines intercept at (1,1), it must satisfy the equation

For Line K : 1 = Mk.1 +Ck
For Line L : 1 = Ml.1 + Cl

=> Mk + Ck = Ml + Cl ------ (equation I)

Now, From Statement 1 - Mk > Ml. Thus, for equation I to hold true. Y intercept of line k must be less than Y intercept of line l (Ck < Cl). Therefore Statement 1 is Sufficient.

Statement 2: Is not sufficient as it doesn't provide information regarding the slope of line L.
##### General Discussion
Director  S
Joined: 09 Jun 2010
Posts: 798
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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1
never use drawing for this type of question. instead, use algebraic to solve . much more easy
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Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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1
18967mba wrote:
In the xy plane, lines k and l intersect at the point (1,1). Is the y intercept of line k greater than the y intercept of line l?
(1) The slope of k is less than the slope of l
(2) the slope of l is positive

By pre-thinking, I was able to come to the following conclusions:
1. If both l and k have +ve slopes, then the line with the lesser slope will have a higher y intercept
2. If both l and k have -ve slopes, then the line with the greater slope will have the higher y intercept
3. If one of the lines has a +ve slope and the other has a -ve slope, then the line with the -ve slope will have the higher y intercept

Based on these conclusions, I chose D but clearly that is incorrect. Can the experts help me by pointing out what is incorrect in my pre-thinking/ what am I assuming/ or if I am approaching this problem completely wrong...

Source: OG Quant review DS:120

It cannot be D because 2nd part is not sufficient to solve the problem. Let me give you an example, assume that the slope of l is 2 and the slope of k is 1 then the y intercept of l would be -1 and the y intercept of k would be 0. And assume the vice versa then the y intercept of k would be smaller. So the second choice is not sufficient. So the answer is A.
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Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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Hi guys,

I chose C because I did this logically rather than algebraically. I can see c is wrong, but now I think I should have chosen E according to my (flawed) logic.

If I draw the x-y plane and show 2 lines passing through (1,1) I can do that in various ways, depending on the slope. If I make them both positive, then both the statements together would be enough . However, if one of them is positive and one of them is negative, cant the one with the lower slope (i.e. negative slope) have a bigger y intercept depending on the value of the slope?!
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Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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I went with A for the reasoning provided. However, what if one of the lines has the line equation: X=1 and thus lacks y intercept?

Posted from my mobile device
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Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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chetan2u wrote:
nalinnair wrote:
In the $$xy$$-plane, lines $$k$$ and $$l$$ intersect at the point $$(1,1)$$. Is the $$y$$-intercept of $$k$$ greater than the $$y$$-intercept of $$l$$?

(1) The slope of $$k$$ is less than the slope of $$l$$.
(2) The slope of $$l$$ is positive.

Hi,

An easy question if you are aware of the slopes....

slope is the Increase in Y/ Increase in X.......... OR Vertical increase / Horizontal increase..

If BOTH increase with increase in each other, the SLOPE is Positive... But if Y decreases with increase in X, slope is -ive....
so for a point (1,1), a line intercepting above Y as 1, it is -ive and with increase in Y, the slope will have even lesser value...
At y=1, slope is 0 and at y<1, the slopw will keep increasing as the value of Y increases...

So the relation of y-intercept is dependent on slope.. lesser the slope higher is the intercept..

(1) The slope of $$k$$ is less than the slope of $$l$$.
As seen above y intercept of line l will be more than line k...
Suff

(2) The slope of $$l$$ is positive.
we require to know slope of line k also
Insuff

A

Bumping this post
actually i am not really good at solving coordinate geo questions so i am just clearing my concepts
as we know that m= -b/x and x for both lines is 1 thus the formula for lines k and l will become m=-b
mk= -bk (slope of line k) and ml+ -bl (slope of line l)
as from statement one we know that mk < ml thus -bk< -bl
am i right?
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Joined: 05 Jul 2006
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Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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9
nalinnair wrote:
In the $$xy$$-plane, lines $$k$$ and $$l$$ intersect at the point $$(1,1)$$. Is the $$y$$-intercept of $$k$$ greater than the $$y$$-intercept of $$l$$?

(1) The slope of $$k$$ is less than the slope of $$l$$.
(2) The slope of $$l$$ is positive.

first line equation 1= m+c , second line equation 1 = n+b , question asks whether c>b

from equations

c = 1-m , b = 1-n , therefore we need relation between the 2 slopes to solve

from 1 m>n this (1-m) < ( 1-n) and therefore b>c... suff

from 2

we have only one slope and no relation between 2 slopes ( insuff)

A
Intern  B
Joined: 18 Mar 2017
Posts: 38
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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chetan2u wrote:
nalinnair wrote:
In the $$xy$$-plane, lines $$k$$ and $$l$$ intersect at the point $$(1,1)$$. Is the $$y$$-intercept of $$k$$ greater than the $$y$$-intercept of $$l$$?

(1) The slope of $$k$$ is less than the slope of $$l$$.
(2) The slope of $$l$$ is positive.

Hi,

An easy question if you are aware of the slopes....

slope is the Increase in Y/ Increase in X.......... OR Vertical increase / Horizontal increase..

If BOTH increase with increase in each other, the SLOPE is Positive... But if Y decreases with increase in X, slope is -ive....
so for a point (1,1), a line intercepting above Y as 1, it is -ive and with increase in Y, the slope will have even lesser value...
At y=1, slope is 0 and at y<1, the slopw will keep increasing as the value of Y increases...

So the relation of y-intercept is dependent on slope.. lesser the slope higher is the intercept..

(1) The slope of $$k$$ is less than the slope of $$l$$.
As seen above y intercept of line l will be more than line k...
Suff

(2) The slope of $$l$$ is positive.
we require to know slope of line k also
Insuff

A

Hi chetan2u I do still struggle with this task and would appreciate your help very much on the following question:

You said the the lesser the slope is the higher is the y-intercept - that makes totally sense to me.
Statement 1 now tells us that the slope of k is less than the slope of m. So according to your explanation k should have a higher y intercept than l (as its slope is less). But you say the opposite: l has a higher y intercept that k?

Thanks for your explanation.

Guenther
Intern  B
Joined: 07 Oct 2016
Posts: 12
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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chetan2u wrote:
nalinnair wrote:
In the $$xy$$-plane, lines $$k$$ and $$l$$ intersect at the point $$(1,1)$$. Is the $$y$$-intercept of $$k$$ greater than the $$y$$-intercept of $$l$$?

(1) The slope of $$k$$ is less than the slope of $$l$$.
(2) The slope of $$l$$ is positive.

Hi,

An easy question if you are aware of the slopes....

slope is the Increase in Y/ Increase in X.......... OR Vertical increase / Horizontal increase..

If BOTH increase with increase in each other, the SLOPE is Positive... But if Y decreases with increase in X, slope is -ive....
so for a point (1,1), a line intercepting above Y as 1, it is -ive and with increase in Y, the slope will have even lesser value...
At y=1, slope is 0 and at y<1, the slopw will keep increasing as the value of Y increases...

So the relation of y-intercept is dependent on slope.. lesser the slope higher is the intercept..

(1) The slope of $$k$$ is less than the slope of $$l$$.
As seen above y intercept of line l will be more than line k...
Suff

(2) The slope of $$l$$ is positive.
we require to know slope of line k also
Insuff

A

Hello bro,
I just don't understand, how y-intercept is lesser if the slope is higher?
Intern  Joined: 07 Jun 2017
Posts: 9
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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1
@bunuel ,

Can you please explain this question in the easiest way possible?

How is statement 1 sufficient? Don't we need the direction of slope as well?

Case 1) both negative - Higher y intercept for line with GREATER slope
Case 2) both positive - higher y intercept for line with LESSER slope
Case 3) one positive one negative ; higher y intercept for line with LESSER slope
Director  G
Joined: 29 Jun 2017
Posts: 598
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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1
for question of this type. there are two ways to solve.
using algebra
or
drawing the lines.

for some questions, we draw to solve , making it easy. for other, we use algebra. which way to use, depending on problem.

hard one
Intern  B
Joined: 09 Dec 2013
Posts: 27
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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maliyeci wrote:
18967mba wrote:
In the xy plane, lines k and l intersect at the point (1,1). Is the y intercept of line k greater than the y intercept of line l?
(1) The slope of k is less than the slope of l
(2) the slope of l is positive

By pre-thinking, I was able to come to the following conclusions:
1. If both l and k have +ve slopes, then the line with the lesser slope will have a higher y intercept
2. If both l and k have -ve slopes, then the line with the greater slope will have the higher y intercept
3. If one of the lines has a +ve slope and the other has a -ve slope, then the line with the -ve slope will have the higher y intercept

Based on these conclusions, I chose D but clearly that is incorrect. Can the experts help me by pointing out what is incorrect in my pre-thinking/ what am I assuming/ or if I am approaching this problem completely wrong...

Source: OG Quant review DS:120

It cannot be D because 2nd part is not sufficient to solve the problem. Let me give you an example, assume that the slope of l is 2 and the slope of k is 1 then the y intercept of l would be -1 and the y intercept of k would be 0. And assume the vice versa then the y intercept of k would be smaller. So the second choice is not sufficient. So the answer is A.

In Case 1 and 2 it is proving that Y intercept of K<L but,
In the third Case where one line is positive and other negative, how is it proving that Y Intercept of K<L.
When K has a +ve slope and L has a -ve the Y Int of K<L, But when L is +ve and K is -ve Y int of K>L. So it is insufficient?
Manager  G
Joined: 14 Oct 2012
Posts: 162
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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chetan2u wrote:
nalinnair wrote:
In the $$xy$$-plane, lines $$k$$ and $$l$$ intersect at the point $$(1,1)$$. Is the $$y$$-intercept of $$k$$ greater than the $$y$$-intercept of $$l$$?

(1) The slope of $$k$$ is less than the slope of $$l$$.
(2) The slope of $$l$$ is positive.

Hi,

An easy question if you are aware of the slopes....

slope is the Increase in Y/ Increase in X.......... OR Vertical increase / Horizontal increase..

If BOTH increase with increase in each other, the SLOPE is Positive... But if Y decreases with increase in X, slope is -ive....
so for a point (1,1), a line intercepting above Y as 1, it is -ive and with increase in Y, the slope will have even lesser value...
At y=1, slope is 0 and at y<1, the slopw will keep increasing as the value of Y increases...

So the relation of y-intercept is dependent on slope.. lesser the slope higher is the intercept..

(1) The slope of $$k$$ is less than the slope of $$l$$.
As seen above y intercept of line l will be more than line k...
Suff

(2) The slope of $$l$$ is positive.
we require to know slope of line k also
Insuff

A

I know that my image is just a rough scribbling, but reading it along side chetan2u explanation should help - if not please let me know...
Thanks
Attachments my 2 cents.png [ 4.09 MiB | Viewed 10544 times ]

Manager  B
Joined: 07 Jun 2017
Posts: 100
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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1
gary391 wrote:
We can write the equation of the line in slope-intercept form as follow: [Where M is the slope and C is the y-intercept]

For Line K : Yk = Mk.Xk +Ck
For Line L : Yl = Ml.Xl + Cl

Now, since these lines intercept at (1,1), it must satisfy the equation

For Line K : 1 = Mk.1 +Ck
For Line L : 1 = Ml.1 + Cl

=> Mk + Ck = Ml + Cl ------ (equation I)

Now, From Statement 1 - Mk > Ml. Thus, for equation I to hold true. Y intercept of line k must be less than Y intercept of line l (Ck < Cl). Therefore Statement 1 is Sufficient.

Statement 2: Is not sufficient as it doesn't provide information regarding the slope of line L.

Dear Gary,
I found your solution the easiest to understand,
however, can you give me the formula of that equation? (1=M+C)< ?
Thank you so much
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Posts: 81
Location: India
Concentration: Operations, Finance
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Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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chetan2u wrote:
nalinnair wrote:
In the $$xy$$-plane, lines $$k$$ and $$l$$ intersect at the point $$(1,1)$$. Is the $$y$$-intercept of $$k$$ greater than the $$y$$-intercept of $$l$$?

(1) The slope of $$k$$ is less than the slope of $$l$$.
(2) The slope of $$l$$ is positive.

Hi,

An easy question if you are aware of the slopes....

slope is the Increase in Y/ Increase in X.......... OR Vertical increase / Horizontal increase..

If BOTH increase with increase in each other, the SLOPE is Positive... But if Y decreases with increase in X, slope is -ive....
so for a point (1,1), a line intercepting above Y as 1, it is -ive and with increase in Y, the slope will have even lesser value...
At y=1, slope is 0 and at y<1, the slopw will keep increasing as the value of Y increases...

So the relation of y-intercept is dependent on slope.. lesser the slope higher is the intercept..

(1) The slope of $$k$$ is less than the slope of $$l$$.
As seen above y intercept of line l will be more than line k...
Suff

(2) The slope of $$l$$ is positive.
we require to know slope of line k also
Insuff

A

When we talk about slope and y-intercept, are we talking about the magnitude of slope and absolute value?

Could someone explain this question in detail?
Manager  G
Joined: 14 Oct 2012
Posts: 162
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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sarathgopinath wrote:
chetan2u wrote:
nalinnair wrote:
In the $$xy$$-plane, lines $$k$$ and $$l$$ intersect at the point $$(1,1)$$. Is the $$y$$-intercept of $$k$$ greater than the $$y$$-intercept of $$l$$?

(1) The slope of $$k$$ is less than the slope of $$l$$.
(2) The slope of $$l$$ is positive.

Hi,

An easy question if you are aware of the slopes....

slope is the Increase in Y/ Increase in X.......... OR Vertical increase / Horizontal increase..

If BOTH increase with increase in each other, the SLOPE is Positive... But if Y decreases with increase in X, slope is -ive....
so for a point (1,1), a line intercepting above Y as 1, it is -ive and with increase in Y, the slope will have even lesser value...
At y=1, slope is 0 and at y<1, the slopw will keep increasing as the value of Y increases...

So the relation of y-intercept is dependent on slope.. lesser the slope higher is the intercept..

(1) The slope of $$k$$ is less than the slope of $$l$$.
As seen above y intercept of line l will be more than line k...
Suff

(2) The slope of $$l$$ is positive.
we require to know slope of line k also
Insuff

A

When we talk about slope and y-intercept, are we talking about the magnitude of slope and absolute value?

Could someone explain this question in detail?

Here we are NOT attempting to find any absolute value or even any magnitude. Here we just using RELATIONS between the slope and y-intercept to answer the question. We WON'T be able to find either magnitude or absolute value. Please read the chetan2u along the image i have uploaded and it might help you. That's how i had solved it. chetan2u explanation is perfect for a question as this one.
Thanks
Intern  B
Joined: 28 Dec 2010
Posts: 23
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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pclawong wrote:
gary391 wrote:
We can write the equation of the line in slope-intercept form as follow: [Where M is the slope and C is the y-intercept]

For Line K : Yk = Mk.Xk +Ck
For Line L : Yl = Ml.Xl + Cl

Now, since these lines intercept at (1,1), it must satisfy the equation

For Line K : 1 = Mk.1 +Ck
For Line L : 1 = Ml.1 + Cl

=> Mk + Ck = Ml + Cl ------ (equation I)

Now, From Statement 1 - Mk > Ml. Thus, for equation I to hold true. Y intercept of line k must be less than Y intercept of line l (Ck < Cl). Therefore Statement 1 is Sufficient.

Statement 2: Is not sufficient as it doesn't provide information regarding the slope of line L.

Dear Gary,
I found your solution the easiest to understand,
however, can you give me the formula of that equation? (1=M+C)< ?
Thank you so much

Thanks pclawong,

To answer your question general equation for a slope intercept form is y = mx + c, where m is the slope, c is the y intercept. In the question stem we are given that the line passes through the (1,1) it should satisfy the equation, therefore 1 = M(1) + C.
Intern  B
Joined: 28 Dec 2010
Posts: 23
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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chetan2u wrote:
nalinnair wrote:
In the $$xy$$-plane, lines $$k$$ and $$l$$ intersect at the point $$(1,1)$$. Is the $$y$$-intercept of $$k$$ greater than the $$y$$-intercept of $$l$$?

(1) The slope of $$k$$ is less than the slope of $$l$$.
(2) The slope of $$l$$ is positive.

Hi,

An easy question if you are aware of the slopes....

slope is the Increase in Y/ Increase in X.......... OR Vertical increase / Horizontal increase..

If BOTH increase with increase in each other, the SLOPE is Positive... But if Y decreases with increase in X, slope is -ive....
so for a point (1,1), a line intercepting above Y as 1, it is -ive and with increase in Y, the slope will have even lesser value...
At y=1, slope is 0 and at y<1, the slopw will keep increasing as the value of Y increases...

So the relation of y-intercept is dependent on slope.. lesser the slope higher is the intercept..

(1) The slope of $$k$$ is less than the slope of $$l$$.
As seen above y intercept of line l will be more than line k...
Suff

(2) The slope of $$l$$ is positive.
we require to know slope of line k also
Insuff

A

Thanks, chetan2u great response. I am trying to understand the relationship of the slope and y intercept. I think irrespective of the line is increasing or decreasing the slope defines lines steepness w.r.t the y -axis. Thus, as we increase the slope our y -intercept should increase. [considering both the line don't have a common intersecting point on the y-axis]. Please let me know if my understanding is correct? Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-   [#permalink] 06 Aug 2017, 11:39

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