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Lines n and p lie in the xyplane. Is the slope of line n [#permalink]
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Lines n and p lie in the xyplane. Is the slope of line n less than the slope of line p ? (1) Lines n and p intersect at the point (5 , 1). (2) The yintercept of line n is greater than the yintercept of line p.
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Re: Lines n and p lie in the xyplane. Is the slope of line n [#permalink]
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BANON wrote: Lines n and p lie in the xyplane. Is the slope of line n less than the slope of line p ?
(1) Lines n and p intersect at the point (5 , 1). (2) The yintercept of line n is greater than the yintercept of line p. Algebraic approach:Lines n and p lie in the xyplane. Is the slope of line n less than the slope of line p?We have two lines: \(y_n=m_1x+b_1\) and \(y_p=m_2x+b_2\). Q: \(m_1<m_2\) true? (1) Lines n and p intersect at the point (5,1) > \(1=5m_1+b_1=5m_2+b_2\) > \(5(m_1m_2)=b_2b_1\). Not sufficient. (2) The yintercept of line \(n\) is greater than the yintercept of line \(p\) > yintercept is value of \(y\) for \(x=0\), so it's the value of \(b\) > \(b_1>b_2\) or \(b_2b_1<0\). Not sufficient. (1)+(2) \(5(m_1m_2)=b_2b_1\), as from (2) \(b_2b_1<0\) (RHS), then LHS (left hand side) also is less than zero \(5(m_1m_2)<0\) > \(m_1m_2<0\) > \(m_1<m_2\). Sufficient. Answer: C. For more on this topic check Coordinate Geometry Chapter of Math Book: mathcoordinategeometry87652.htmlHope it helps.
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Lines n and p lie in the xyplane. Is the slope of line n [#permalink]
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23 Feb 2012, 07:13
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BANON wrote: Lines n and p lie in the xyplane. Is the slope of line n less than the slope of line p ?
(1) Lines n and p intersect at the point (5 , 1). (2) The yintercept of line n is greater than the yintercept of line p. Graphic approach:Lines n and p lie in the xy plane. Is the slope of line n less than the slope of line p?(1) Lines n and p intersect at (5,1) (2) The yintercept of line n is greater than yintercept of line p The two statements individually are not sufficient. (1)+(2) Note that a higher absolute value of a slope indicates a steeper incline. Now, if both lines have positive slopes then as the yintercept of line n (blue) is greater than yintercept of line p (red) then the line p is steeper hence its slope is greater than the slope of the line n: If both lines have negative slopes then again as the yintercept of line n (blue) is greater than yintercept of line p (red) then the line n is steeper hence the absolute value of its slope is greater than the absolute value of the slope of the line p, so the slope of n is more negative than the slope of p, which means that the slope of p is greater than the slope of n: So in both cases the slope of p is greater than the slope of n. Sufficient. Answer: C. Attachment:
1.PNG [ 14.29 KiB  Viewed 23551 times ]
Attachment:
2.PNG [ 13.66 KiB  Viewed 23534 times ]
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Re: Lines n and p lie in the xyplane. Is the slope of line n [#permalink]
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23 Feb 2012, 08:05
Bunuel,
What if line p has a negative y intercept but line n has a positive intercept? Wouldn't that give the oposite answer?



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Re: Lines n and p lie in the xyplane. Is the slope of line n le [#permalink]
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13 Sep 2012, 11:19
monikaleoster wrote: Lines n and p lie in the xyplane. Is the slope of line n less than the slope of line p ? (1) Lines n and p intersect at the point (5,1). (2) The yintercept of line n is greater than the yintercept of line p. Here we have two lines and two slopes So lets first write the equations for our lovely lines Y = mnX + Cn Y = mpX + Cp Now statement one says that it intersects at 5,1. SO lets put it in the equations and subtract them We get, (mnmp)5 = CpCn that tells us nothing about the slopes of the lines or their relative values, but if we know the value of CpCn that weather it is positive or negative we will know weathet mnmp is positive or negative and that which is greater Statement 2 Y intercept of line n is greater than p so that gives us Cn >Cp Alone this statement is also not sufficient. it talks abou c not slopes But if we combine the two, Voila !! we know which slope is greater.



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Re: Lines n and p lie in the xyplane. Is the slope of line n [#permalink]
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29 Dec 2012, 08:18
I don't get it :/
what if slope of line P is positive and the slope of line N negative (but still satisfying all the condition...) Bunuel, on your examples the slopes have the same sign... are we talking about the absolute value of the slope?



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Re: Lines n and p lie in the xyplane. Is the slope of line n [#permalink]
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27 Jun 2013, 21:29



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Re: Lines n and p lie in the xyplane. Is the slope of line n [#permalink]
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16 Jul 2013, 18:23
Bunuel wrote: BANON wrote: Lines n and p lie in the xyplane. Is the slope of line n less than the slope of line p ?
(1) Lines n and p intersect at the point (5 , 1). (2) The yintercept of line n is greater than the yintercept of line p. Algebraic approach:Lines n and p lie in the xyplane. Is the slope of line n less than the slope of line p?We have two lines: \(y_n=m_1x+b_1\) and \(y_p=m_2x+b_2\). Q: \(m_1<m_2\) true? (1) Lines n and p intersect at the point (5,1) > \(1=5m_1+b_1=5m_2+b_2\) > \(5(m_1m_2)=b_2b_1\). Not sufficient. (2) The yintercept of line \(n\) is greater than the yintercept of line \(p\) > yintercept is value of \(y\) for \(x=0\), so it's the value of \(b\) > \(b_1>b_2\) or \(b_2b_1<0\). Not sufficient. (1)+(2) \(5(m_1m_2)=b_2b_1\), as from (2) \(b_2b_1<0\) (RHS), then LHS (left hand side) also is less than zero \(5(m_1m_2)<0\) > \(m_1m_2<0\) > \(m_1<m_2\). Sufficient. Answer: C. Hope it helps. Bunuel, In here  \(y_n=m_1x+b_1\) and \(y_p=m_2x+b_2\). Q: \(m_1<m_2\) true? Why have you chosen different variables for the y? Shouldnt the two equations be y=m1x+b1 and y=m2x+b2? We always form the equation from the basic form of y=mx+c wherein we substitute the values of m and c. And if that is the case, we can get the answer from statement II only. I know I am missing something but I am not clear as to why you have picked different variables for y but not for x.



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Re: Lines n and p lie in the xyplane. Is the slope of line n [#permalink]
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16 Jul 2013, 22:08
keenys wrote: Bunuel wrote: BANON wrote: Lines n and p lie in the xyplane. Is the slope of line n less than the slope of line p ?
(1) Lines n and p intersect at the point (5 , 1). (2) The yintercept of line n is greater than the yintercept of line p. Algebraic approach:Lines n and p lie in the xyplane. Is the slope of line n less than the slope of line p?We have two lines: \(y_n=m_1x+b_1\) and \(y_p=m_2x+b_2\). Q: \(m_1<m_2\) true? (1) Lines n and p intersect at the point (5,1) > \(1=5m_1+b_1=5m_2+b_2\) > \(5(m_1m_2)=b_2b_1\). Not sufficient. (2) The yintercept of line \(n\) is greater than the yintercept of line \(p\) > yintercept is value of \(y\) for \(x=0\), so it's the value of \(b\) > \(b_1>b_2\) or \(b_2b_1<0\). Not sufficient. (1)+(2) \(5(m_1m_2)=b_2b_1\), as from (2) \(b_2b_1<0\) (RHS), then LHS (left hand side) also is less than zero \(5(m_1m_2)<0\) > \(m_1m_2<0\) > \(m_1<m_2\). Sufficient. Answer: C. Hope it helps. Bunuel, In here  \(y_n=m_1x+b_1\) and \(y_p=m_2x+b_2\). Q: \(m_1<m_2\) true? Why have you chosen different variables for the y? Shouldnt the two equations be y=m1x+b1 and y=m2x+b2? We always form the equation from the basic form of y=mx+c wherein we substitute the values of m and c. And if that is the case, we can get the answer from statement II only. I know I am missing something but I am not clear as to why you have picked different variables for y but not for x. n and p are subscripts of y's, not variables. \(y=m_1x+b_1\) is equation of line n. \(y=m_2x+b_2\) is equation of line p. I used subscripts simply to distinguish one equation from another.
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Re: Lines n and p lie in the xyplane. Is the slope of line n [#permalink]
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17 Jul 2013, 04:02
Bunuel wrote: keenys wrote: Bunuel wrote: Algebraic approach:
Lines n and p lie in the xyplane. Is the slope of line n less than the slope of line p?
We have two lines: \(y_n=m_1x+b_1\) and \(y_p=m_2x+b_2\). Q: \(m_1<m_2\) true?
(1) Lines n and p intersect at the point (5,1) > \(1=5m_1+b_1=5m_2+b_2\) > \(5(m_1m_2)=b_2b_1\). Not sufficient. (2) The yintercept of line \(n\) is greater than the yintercept of line \(p\) > yintercept is value of \(y\) for \(x=0\), so it's the value of \(b\) > \(b_1>b_2\) or \(b_2b_1<0\). Not sufficient.
(1)+(2) \(5(m_1m_2)=b_2b_1\), as from (2) \(b_2b_1<0\) (RHS), then LHS (left hand side) also is less than zero \(5(m_1m_2)<0\) > \(m_1m_2<0\) > \(m_1<m_2\). Sufficient.
Answer: C.
Hope it helps.
Bunuel, In here  \(y_n=m_1x+b_1\) and \(y_p=m_2x+b_2\). Q: \(m_1<m_2\) true? Why have you chosen different variables for the y? Shouldnt the two equations be y=m1x+b1 and y=m2x+b2? We always form the equation from the basic form of y=mx+c wherein we substitute the values of m and c. And if that is the case, we can get the answer from statement II only. I know I am missing something but I am not clear as to why you have picked different variables for y but not for x. n and p are subscripts of y's, not variables. \(y=m_1x+b_1\) is equation of line n. \(y=m_2x+b_2\) is equation of line p. I used subscripts simply to distinguish one equation from another. If that is the case then, from the above equations we get b1=ym1x and b2=ym2x Now from statement 2 we know that b1>b2... therefore, ym1x >ym2x which gives (m1m2)x>0 So it can be proved from statement 2 only that m1>m2 Where am I going wrong?



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Re: Lines n and p lie in the xyplane. Is the slope of line n [#permalink]
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17 Jul 2013, 05:07
keenys wrote: Bunuel wrote: keenys wrote: Bunuel,
In here  \(y_n=m_1x+b_1\) and \(y_p=m_2x+b_2\). Q: \(m_1<m_2\) true?
Why have you chosen different variables for the y?
Shouldnt the two equations be y=m1x+b1 and y=m2x+b2? We always form the equation from the basic form of y=mx+c wherein we substitute the values of m and c. And if that is the case, we can get the answer from statement II only.
I know I am missing something but I am not clear as to why you have picked different variables for y but not for x. n and p are subscripts of y's, not variables. \(y=m_1x+b_1\) is equation of line n. \(y=m_2x+b_2\) is equation of line p. I used subscripts simply to distinguish one equation from another. If that is the case then, from the above equations we get b1=ym1x and b2=ym2x Now from statement 2 we know that b1>b2... therefore, ym1x >ym2x which gives (m1m2)x>0 So it can be proved from statement 2 only that m1>m2 Where am I going wrong? The yintercept is the value of \(y\) for \(x=0\). You should substitute x=0 into both equations. So, the yintercept of line n is b1 and the yintercept of line p is b2, from (2) we only have that b1>b2.
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Re: Lines n and p lie in the xyplane. Is the slope of line n [#permalink]
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28 Dec 2013, 04:57
Bunuel wrote: BANON wrote: Lines n and p lie in the xyplane. Is the slope of line n less than the slope of line p ?
(1) Lines n and p intersect at the point (5 , 1). (2) The yintercept of line n is greater than the yintercept of line p. Graphic approach:Lines n and p lie in the xy plane. Is the slope of line n less than the slope of line p?(1) Lines n and p intersect at (5,1) (2) The yintercept of line n is greater than yintercept of line p The two statements individually are not sufficient. (1)+(2) Note that a higher absolute value of a slope indicates a steeper incline. Now, if both lines have positive slopes then as the yintercept of line n (blue) is greater than yintercept of line p (red) then the line p is steeper hence its slope is greater than the slope of the line n: Attachment: 1.PNG If both lines have negative slopes then again as the yintercept of line n (blue) is greater than yintercept of line p (red) then the line n is steeper hence the absolute value of its slope is greater than the absolute value of the slope of the line p, so the slope of n is more negative than the slope of p, which means that the slope of p is greater than the slope of n: Attachment: 2.PNG So in both cases the slope of p is greater than the slope of n. Sufficient. Answer: C. So talking about the case with negative slopes here. OK so line 'n' is steeper hence it has a higher absolute value for slope right? Then because it is more negative then it is in fact smaller than the slope of line p. So here we are saying that the slope is treated just as any number, which means considering its sign Eg. Slope of an horizontal line will be higher than a negative slope right? Just cause if one does it algebraically one will encounter the comparison and absolute values are not used at all in slope formulae as far as I'm aware Just wanted to get this straight Please advice Cheers! J



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Re: Lines n and p lie in the xyplane. Is the slope of line n [#permalink]
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02 Sep 2014, 02:54
Bunuel wrote: BANON wrote: Lines n and p lie in the xyplane. Is the slope of line n less than the slope of line p ?
(1) Lines n and p intersect at the point (5 , 1). (2) The yintercept of line n is greater than the yintercept of line p. Algebraic approach:Lines n and p lie in the xyplane. Is the slope of line n less than the slope of line p?We have two lines: \(y_n=m_1x+b_1\) and \(y_p=m_2x+b_2\). Q: \(m_1<m_2\) true? (1) Lines n and p intersect at the point (5,1) > \(1=5m_1+b_1=5m_2+b_2\) > \(5(m_1m_2)=b_2b_1\). Not sufficient. (2) The yintercept of line \(n\) is greater than the yintercept of line \(p\) > yintercept is value of \(y\) for \(x=0\), so it's the value of \(b\) > \(b_1>b_2\) or \(b_2b_1<0\). Not sufficient. (1)+(2) \(5(m_1m_2)=b_2b_1\), as from (2) \(b_2b_1<0\) (RHS), then LHS (left hand side) also is less than zero \(5(m_1m_2)<0\) > \(m_1m_2<0\) > \(m_1<m_2\). Sufficient. Answer: C. For more on this topic check Coordinate Geometry Chapter of Math Book: mathcoordinategeometry87652.htmlHope it helps. Hi Bunuel Pl clarify my doubt. Do we need to consider absolute values for slopes? I mean is it m1<m2 ? or m1<m2? to consider



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Re: Lines n and p lie in the xyplane. Is the slope of line n [#permalink]
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02 Sep 2014, 03:25
Sidhrt wrote: Bunuel wrote: BANON wrote: Lines n and p lie in the xyplane. Is the slope of line n less than the slope of line p ?
(1) Lines n and p intersect at the point (5 , 1). (2) The yintercept of line n is greater than the yintercept of line p. Algebraic approach:Lines n and p lie in the xyplane. Is the slope of line n less than the slope of line p?We have two lines: \(y_n=m_1x+b_1\) and \(y_p=m_2x+b_2\). Q: \(m_1<m_2\) true? (1) Lines n and p intersect at the point (5,1) > \(1=5m_1+b_1=5m_2+b_2\) > \(5(m_1m_2)=b_2b_1\). Not sufficient. (2) The yintercept of line \(n\) is greater than the yintercept of line \(p\) > yintercept is value of \(y\) for \(x=0\), so it's the value of \(b\) > \(b_1>b_2\) or \(b_2b_1<0\). Not sufficient. (1)+(2) \(5(m_1m_2)=b_2b_1\), as from (2) \(b_2b_1<0\) (RHS), then LHS (left hand side) also is less than zero \(5(m_1m_2)<0\) > \(m_1m_2<0\) > \(m_1<m_2\). Sufficient. Answer: C. For more on this topic check Coordinate Geometry Chapter of Math Book: mathcoordinategeometry87652.htmlHope it helps. Hi Bunuel Pl clarify my doubt. Do we need to consider absolute values for slopes? I mean is it m1<m2 ? or m1<m2? to consider The question asks whether \(m_1<m_2\).
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Re: Lines n and p lie in the xyplane. Is the slope of line n [#permalink]
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02 Sep 2014, 03:33
Sidhrt wrote: Bunuel wrote: BANON wrote: Lines n and p lie in the xyplane. Is the slope of line n less than the slope of line p ?
(1) Lines n and p intersect at the point (5 , 1). (2) The yintercept of line n is greater than the yintercept of line p. Algebraic approach:Lines n and p lie in the xyplane. Is the slope of line n less than the slope of line p?We have two lines: \(y_n=m_1x+b_1\) and \(y_p=m_2x+b_2\). Q: \(m_1<m_2\) true? (1) Lines n and p intersect at the point (5,1) > \(1=5m_1+b_1=5m_2+b_2\) > \(5(m_1m_2)=b_2b_1\). Not sufficient. (2) The yintercept of line \(n\) is greater than the yintercept of line \(p\) > yintercept is value of \(y\) for \(x=0\), so it's the value of \(b\) > \(b_1>b_2\) or \(b_2b_1<0\). Not sufficient. (1)+(2) \(5(m_1m_2)=b_2b_1\), as from (2) \(b_2b_1<0\) (RHS), then LHS (left hand side) also is less than zero \(5(m_1m_2)<0\) > \(m_1m_2<0\) > \(m_1<m_2\). Sufficient. Answer: C. For more on this topic check Coordinate Geometry Chapter of Math Book: mathcoordinategeometry87652.htmlHope it helps. Hi Bunuel Pl clarify my doubt. Do we need to consider absolute values for slopes? I mean is it m1<m2 ? or m1<m2? to consider then without taking absolute values how we can conclude m1<m2? as we not sure m1<0 or m1>0 or m2<0 or m2>0 ( such as m1=1, m2=5 or m2=5,m1=1)



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Re: Lines n and p lie in the xyplane. Is the slope of line n [#permalink]
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02 Sep 2014, 03:54
Sidhrt wrote: Sidhrt wrote: Bunuel wrote: Algebraic approach:Lines n and p lie in the xyplane. Is the slope of line n less than the slope of line p?We have two lines: \(y_n=m_1x+b_1\) and \(y_p=m_2x+b_2\). Q: \(m_1<m_2\) true? (1) Lines n and p intersect at the point (5,1) > \(1=5m_1+b_1=5m_2+b_2\) > \(5(m_1m_2)=b_2b_1\). Not sufficient. (2) The yintercept of line \(n\) is greater than the yintercept of line \(p\) > yintercept is value of \(y\) for \(x=0\), so it's the value of \(b\) > \(b_1>b_2\) or \(b_2b_1<0\). Not sufficient. (1)+(2) \(5(m_1m_2)=b_2b_1\), as from (2) \(b_2b_1<0\) (RHS), then LHS (left hand side) also is less than zero \(5(m_1m_2)<0\) > \(m_1m_2<0\) > \(m_1<m_2\). Sufficient. Answer: C. For more on this topic check Coordinate Geometry Chapter of Math Book: mathcoordinategeometry87652.htmlHope it helps. Hi Bunuel Pl clarify my doubt. Do we need to consider absolute values for slopes? I mean is it m1<m2 ? or m1<m2? to consider then without taking absolute values how we can conclude m1<m2? as we not sure m1<0 or m1>0 or m2<0 or m2>0 ( such as m1=1, m2=5 or m2=5,m1=1) Dear Sidhrt, there are two approaches given above explaining that.
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Lines n and p lie in the xyplane. Is the slope of line n [#permalink]
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06 Jan 2016, 12:43
BANON wrote: Lines n and p lie in the xyplane. Is the slope of line n less than the slope of line p ?
(1) Lines n and p intersect at the point (5 , 1). (2) The yintercept of line n is greater than the yintercept of line p. Hi math experts, I've used the following approach to derive on the correct answer. Would appreciate your input. (1) It's not possible to calculate the slope with only one point given. Also it's an intersection point which satisfies the equations of both lines. Not Sufficient (2) You cannot determine a slope, with info about yintercept, one can manipulate randomply the xline intersection and get diff. results regarding slopes. (1)+(2) We have point (5,1) and info about y intercept. By yintercept x=0 and we know that line n has a greater yintercept: Case 1 +ve: Line n (0, 3) and Line p (0, 2) > Slope n \(= \frac{13}{5}=\frac{2}{5}\), Slope p\(=\frac{12}{5}=\frac{1}{5}\), So Slope p > Slope n Case 2 ve: Line n (0, 2) and Line p (0, 3) > Slope n \(= \frac{1(2)}{5}=\frac{3}{5}\), Slope p=\(\frac{1(3)}{5}=\frac{4}{5}\) Again Slope p > Slope n Answer C
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Re: Lines n and p lie in the xyplane. Is the slope of line n [#permalink]
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10 Mar 2016, 21:36
Bunuel wrote: BANON wrote: Lines n and p lie in the xyplane. Is the slope of line n less than the slope of line p ?
(1) Lines n and p intersect at the point (5 , 1). (2) The yintercept of line n is greater than the yintercept of line p. Graphic approach:Lines n and p lie in the xy plane. Is the slope of line n less than the slope of line p?(1) Lines n and p intersect at (5,1) (2) The yintercept of line n is greater than yintercept of line p The two statements individually are not sufficient. (1)+(2) Note that a higher absolute value of a slope indicates a steeper incline. Now, if both lines have positive slopes then as the yintercept of line n (blue) is greater than yintercept of line p (red) then the line p is steeper hence its slope is greater than the slope of the line n: Attachment: 1.PNG If both lines have negative slopes then again as the yintercept of line n (blue) is greater than yintercept of line p (red) then the line n is steeper hence the absolute value of its slope is greater than the absolute value of the slope of the line p, so the slope of n is more negative than the slope of p, which means that the slope of p is greater than the slope of n: Attachment: 2.PNG So in both cases the slope of p is greater than the slope of n. Sufficient. Answer: C. We have tried both slopes negative or both slopes positive, why we didn't tried one slope positive and another negative combination.
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Lines n and p lie in the xyplane. Is the slope of line n [#permalink]
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10 Oct 2016, 11:01
Bunuel wrote: nglekel wrote: Bunuel,
What if line p has a negative y intercept but line n has a positive intercept? Wouldn't that give the oposite answer? If line p has a negative yintercept then its slope is positive and it will still be more than the slope of n, with positive yintercept (if the slope of n will be positive than p will still be steeper than n, and if the slope of n is negative it obviously will be less than positive slope of p). Consider first image and rotate line n (blue) so that it to have positive yintercept and you'll easily see the answer. Hope it helps. Experts Please reply for my doubt..... for below attached fig ...getting 2 diff.. answers.....
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coordinate.png [ 17.92 KiB  Viewed 3004 times ]




Lines n and p lie in the xyplane. Is the slope of line n
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