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Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y
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07 Aug 2017, 18:37
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 yintercept 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 yaxis]. 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 xyplane, lines k and l intersect at the point (1,1). Is the y
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31 Aug 2017, 22:22
please see the attachment, 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
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Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y
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Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y
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31 Aug 2017, 23:05
Bunuel wrote: pclawong wrote: please see the attachment, 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: 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



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Re: In the xyplane, lines k and l intersect at the point (1,1)
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31 Aug 2017, 23:24
pclawong wrote: Bunuel wrote: pclawong wrote: please see the attachment, 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: 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 yintercept of K is greater than the yintercept of L. For (1) the yintercept of K will always be greater than the yintercept of L.
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Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y
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12 Sep 2017, 06:05
(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
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Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y
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19 Sep 2017, 08:00
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 yintercept 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 yintercept of K always be greater than the yintercept of L?



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Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y
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15 Oct 2017, 09:03
gary391 wrote: We can write the equation of the line in slopeintercept form as follow: [Where M is the slope and C is the yintercept]
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 = 1Ck. Similarly, Ml = 1Cl. Therefore, from statement 1, Mk < Ml => 1Ck < 1  Cl => Ck > Cl



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Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y
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20 Feb 2018, 03:59
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 xyplane, lines k and l intersect at the point (1,1). Is the y
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03 Mar 2018, 07:31
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 yintercept for line k ?



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Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y
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05 Mar 2018, 00:13
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 yintercept 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 xyplane, lines k and l intersect at the point (1,1). Is the y
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05 Mar 2018, 00:17
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 yintercept 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 ! ! !Ultimate GMAT Quantitative MegathreadHope it helps.
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Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y
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11 May 2018, 13:31
gary391 wrote: We can write the equation of the line in slopeintercept form as follow: [Where M is the slope and C is the yintercept]
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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In the xyplane, lines k and l intersect at the point (1,1). Is the y
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02 Nov 2018, 02:08
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 363 times ]
Case 2. Positive\(Line K:\)\(y=2x1\)\(Line L:\)\(y=3x2\)Attachment:
2.png [ 27.98 KiB  Viewed 361 times ]
Case 3. \(K\) negative and \(L\) positive\(Line K:\)\(y=2x+3\)\(Line L:\)\(y=3x2\)Attachment:
3.png [ 28.66 KiB  Viewed 361 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 xyplane, lines k and l intersect at the point (1,1). Is the y
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13 Nov 2018, 19:31
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 yintercept 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 xyplane, lines k and l intersect at the point (1,1). Is the y
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22 Dec 2018, 07:38
nalinnair wrote: In the xyplane, lines k and l intersect at the point (1,1). Is the yintercept of k greater than the yintercept of l?
(1) The slope of k is less than the slope of l. (2) The slope of l is positive. Given: In the xyplane, lines k and l intersect at the point (1,1). Target question: Is the yintercept of k greater than the yintercept 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 yintercept of k IS greater than the yintercept 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 yintercept of k IS greater than the yintercept 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 yintercept of k IS greater than the yintercept 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 yintercept of k IS greater than the yintercept of l In both of the above cases, the answer to the target question will be the yintercept of k IS greater than the yintercept of l 00 Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: The slope of l is positive.No information about line k Statement 2 is NOT SUFFICIENT Answer: A Cheers, Brent
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Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y &nbs
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