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Math Expert V
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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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gary391 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

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?

Hi...

If you just take the absolute value, yes with change in x as constant, change in y will be as per your understanding..

The slope depends on change in value of both x and y.
Numerator has change in y, so more the change more the slope
Denominator has change in x, so less the change more the slope

But the slope can be of two types..
From left bottom to right top...... Both change in x and y will be POSITIVE, so slope is POSITIVE
From left top to bottom right......Change in y is NEGATIVE and change in x will be POSITIVE, so slope is -/+= NEGATIVE even if the absolute value or steepness is MORE
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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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let say Ml= -4
Mk= -6
then the slope of k is less than slope of L
y intercept K is greater than L

so I think we need both statement to confirm.
isn't it?

Bunuel or anyone, please correct me
Attachments line.PNG [ 5.52 KiB | Viewed 1925 times ]

Math Expert V
Joined: 02 Sep 2009
Posts: 56277
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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1
pclawong 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.

let say Ml= -4
Mk= -6
then the slope of k is less than slope of L
y intercept K is greater than L

so I think we need both statement to confirm.
isn't it?

Bunuel or anyone, please correct me If the slope of line L is -4 and the slope of line K is -6, the lines won't look like the way you've drawn. The will look like as below: Attachment: Untitled.png [ 10.79 KiB | Viewed 2151 times ]

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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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Bunuel wrote:
pclawong wrote:
let say Ml= -4
Mk= -6
then the slope of k is less than slope of L
y intercept K is greater than L

so I think we need both statement to confirm.
isn't it?

Bunuel or anyone, please correct me

If the slope of line L is -4 and the slope of line K is -6, the lines won't look like the way you've drawn. The will look like as below: Attachment:
Untitled.png

Oh yea, I mean the red line is K
and the blue line is L
so then, even the slope L is larger than slope K,
y intercept of K is still larger than L
am I correct?
that means, statement 1 is not suff.
we also need to know if it is positive slope or negative
Math Expert V
Joined: 02 Sep 2009
Posts: 56277
Re: In the xy-plane, lines k and l intersect at the point (1,1)  [#permalink]

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2
pclawong wrote:
Bunuel wrote:
pclawong wrote:
let say Ml= -4
Mk= -6
then the slope of k is less than slope of L
y intercept K is greater than L

so I think we need both statement to confirm.
isn't it?

Bunuel or anyone, please correct me

If the slope of line L is -4 and the slope of line K is -6, the lines won't look like the way you've drawn. The will look like as below: Attachment:
Untitled.png

Oh yea, I mean the red line is K
and the blue line is L
so then, even the slope L is larger than slope K,
y intercept of K is still larger than L
am I correct?
that means, statement 1 is not suff.
we also need to know if it is positive slope or negative

(1) says that the slope of $$k$$ is less than the slope of $$l$$. So, in my image BLUE line is K (slope -6) and the RED line is L (slope -4).

As you can see the y-intercept of K is greater than the y-intercept of L. For (1) the y-intercept of K will always be greater than the y-intercept of L.
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GMAT 1: 560 Q42 V25 Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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(k): y=a1*x+b1
(l): y=a2*x+b2
Line k and l intersect at(1,1):
a1+b1=a2+b2
(1): a1<a2 => b1> b2 sufficient
(2) a2>0 not sufficient

A

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GMAT 1: 700 Q48 V37 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,

from (1) Shouldn't the value of y-intercept of K always be greater than the y-intercept of L?
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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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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.

You can further refine equation: 1 = Mk + ck => Mk = 1-Ck. Similarly, Ml = 1-Cl. Therefore, from statement 1, Mk < Ml => 1-Ck < 1 - Cl => Ck > Cl
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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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MarkusKarl Asked this on the first page and I have the same question.

I played devils advocate and got E. What if the slope of L is 1 and the slope of K is zero or undefined? Then K would never intercept the axis, correct?

Thanks in advance for the explanation.
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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 agree with msurls, if for line K we have equation X= costant, how do you define the slope and therefore the intercept with Y (which doesn't exist) ? Do you consider the slope of a line parallel to Y axis as +infinite or (-) infinite...? In this case how can you say that 1) is suff, since you don't have any value of y-intercept for line k ?
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Posts: 56277
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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teone83 wrote:
I agree with msurls, if for line K we have equation X= costant, how do you define the slope and therefore the intercept with Y (which doesn't exist) ? Do you consider the slope of a line parallel to Y axis as +infinite or (-) infinite...? In this case how can you say that 1) is suff, since you don't have any value of y-intercept for line k ?

A vertical line has no slope. Or put another way, for a vertical line the slope is undefined. This, by the way, does NOT mean that its slope is 0, horizontal lines has slope equal to 0.

Statement (1) says that "The slope of k is less than the slope of l". If any of the lines were vertical, their slopes would be undefined and it would not make sense to compare an undefined slope to anything. Thus, (1) implies that neither of the lines is vertical.
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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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Bunuel wrote:
teone83 wrote:
I agree with msurls, if for line K we have equation X= costant, how do you define the slope and therefore the intercept with Y (which doesn't exist) ? Do you consider the slope of a line parallel to Y axis as +infinite or (-) infinite...? In this case how can you say that 1) is suff, since you don't have any value of y-intercept for line k ?

A vertical line has no slope. Or put another way, for a vertical line the slope is undefined. This, by the way, does NOT mean that its slope is 0, horizontal lines has slope equal to 0.

Statement (1) says that "The slope of k is less than the slope of l". If any of the lines were vertical, their slopes would be undefined and it would not make sense to compare an undefined slope to anything. Thus, (1) implies that neither of the lines is vertical.

24. Coordinate Geometry

For other subjects:
ALL YOU NEED FOR QUANT ! ! !

Hope it helps.
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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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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.

No offense, but I think that more than 1 person here slightly misread statement 1. In other words, Mk < Ml according to the statement. So, the following is what I think:

From statement 1 ---> Mk < Ml. Thus for equation I to hold true the Y intercept of line k must be > the Y intercept of line l. (Ck > Cl). Therefore, statement 1 is sufficient.
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GMAT 1: 560 Q39 V28 GMAT 2: 670 Q48 V34 In the xy-plane, lines k and l intersect at the point (1,1). Is the y-  [#permalink]

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2
I had a really hard time following and understanding the above discussion... Therefore I tried to use a more graphical approach and see how S(1) is sufficient!

We should consider 3 cases for S(1): Booth slopes are negative, booth slopes are positive, and slope $$K$$ is negative and slope $$L$$ is positive.

Case 1. Negative
$$Line K:$$$$y=-2x+3$$
$$Line L:$$$$y=-1x+2$$
Attachment: 1.png [ 29.34 KiB | Viewed 985 times ]

Case 2. Positive
$$Line K:$$$$y=2x-1$$
$$Line L:$$$$y=3x-2$$
Attachment: 2.png [ 27.98 KiB | Viewed 983 times ]

Case 3. $$K$$ negative and $$L$$ positive
$$Line K:$$$$y=-2x+3$$
$$Line L:$$$$y=3x-2$$
Attachment: 3.png [ 28.66 KiB | Viewed 984 times ]

We can see in every case $$K$$ has a higher y intercept than $$L$$.

Therefore S(1) is sufficient and A is the answer.
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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

Hi Chetu

Thanks for the explanation, though for my understanding please would you confirm ;

"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. "

Does this mean that every line with a negative slope will have a negative y intercept ? @ " 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..."
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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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Top Contributor
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.

Given: In the xy-plane, lines k and l intersect at the point (1,1).

Target question: Is the y-intercept of k greater than the y-intercept of l?

Statement 1: The slope of k is less than the slope of l.
Let's examine 2 cases, and then make a generalization.

CASE A) the slope of line k is POSITIVE
For example, let's say line k has slope 1. If line l has a greater slope (like a slope of 2), we can see that the y-intercept of k IS greater than the y-intercept of l
We can further see that if line l has a slope of 3, 4, 5, 6 etc , it will always be the case that the y-intercept of k IS greater than the y-intercept of l

CASE B) the slope of line k is NEGATIVE
For example, let's say line k has slope -1.5 If line l has a greater slope (like a slope of -0.6), we can see that the y-intercept of k IS greater than the y-intercept of l
We can further see that if line l has a slope that's greater than line k, it will always be the case that the y-intercept of k IS greater than the y-intercept of l

In both of the above cases, the answer to the target question will be the y-intercept of k IS greater than the y-intercept of l 00
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The slope of l is positive.
Statement 2 is NOT SUFFICIENT

Cheers,
Brent
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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

Hi Chetan2u,

Thanks for your explanation, but I still do not understand below statement from yours, could you pleaseexplain further?

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..
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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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y=m1x +c1 --k

y=m2x+ c2 ---l

(x,y)=(1,1)

1=m1 +c1
1=m2 +c2

1) m1<m2

suff

2) NS
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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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GMATPrepNow

I'm having difficulty in understanding the working of this question. By saying the slope is less, does that mean a slope of -1 is less than 1? I understand that one is positive and the other negative but the magnitude of the slope is equivalent and thus I would conclude that the slope is the same.
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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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Top Contributor
amandesai17 wrote:
GMATPrepNow

I'm having difficulty in understanding the working of this question. By saying the slope is less, does that mean a slope of -1 is less than 1? I understand that one is positive and the other negative but the magnitude of the slope is equivalent and thus I would conclude that the slope is the same.

Lines with slopes 1 and -1 have the same STEEPNESS, but the slopes are different.
So, the SLOPE of -1 is less than the SLOPE of 1

Cheers,
Brent
_________________ Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y-   [#permalink] 09 Jul 2019, 06:08

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