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In the xyplane, if line k has negative slope, is the [#permalink]
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14 Mar 2012, 01:04
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In the xyplane, if line k has negative slope, is the yintercept of line k positive? (1) The xintercept of line k is less than the yintercept of line k. (2) The slope of line k is less than 2. It is a DS question, can you help and explain the answer?
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Re: DS coordinate geometry question [#permalink]
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14 Mar 2012, 01:51
vdadwal wrote: In the xyplane, if line k has negative slope, is the yintercept of line k positive?
(1) The xintercept of line k is less than the yintercept of line k.
(2) The slope of line k is less than 2.
It is a DS question, can you help and explain the answer? let me try: we have line k say: y=mx+c we need to find if c>0 1) xintercept, i.e. y=0 x=c/m yintercept, i.e. x=0 y=c hence c/m<c => c*((1/m)+1)>0 i.e. for different value of "m", "c" can be both positive and negative hence insufficient 2) cant infer anything about c insufficient 1+2 if m<2 c*(m+1)<0 (m<0 hence sign change) as m<2 hence m+1<1 i.e. negative i.e. c>0 Sufficient hence C hope it helps..!!!
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Re: DS coordinate geometry question [#permalink]
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14 Mar 2012, 02:07
thanks , i also got the following explanation and dont understand the logic behind their deduction from 1 ,
Explanation
If a line has negative slope, the intercepts will have the same sign. So if we can find the sign of the xintercept, we can answer the question.
Statement (1) is insufficient. It's possible that both intercepts are negative, for instance if the xintercept is 4, the yintercept could be 2. This is a relatively flat slopeas it turns out, it's true if the slope is greater than 1. It's also possible that both intercepts are positive. For instance, if the xintercept is 3, the yintercept could be 5. The negative slope here is steeperin general, less than 1.
Statement (2) is also insufficient. Such a slope is relatively steep, but it could result in positive or negative interceptsthe slope of the line doesn't determine the location of the line.
Taken together, the statements are sufficient. In (1), we learned that if the slope is less than 1, both intercepts are positive. Since the slope is less than 2, both intercepts must be positive. Choice (C) is correct.
Can you help ?
thanks



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Re: DS coordinate geometry question [#permalink]
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14 Mar 2012, 20:11
vdadwal wrote: thanks , i also got the following explanation and dont understand the logic behind their deduction from 1 ,
Explanation
If a line has negative slope, the intercepts will have the same sign. So if we can find the sign of the xintercept, we can answer the question.
Statement (1) is insufficient. It's possible that both intercepts are negative, for instance if the xintercept is 4, the yintercept could be 2. This is a relatively flat slopeas it turns out, it's true if the slope is greater than 1. It's also possible that both intercepts are positive. For instance, if the xintercept is 3, the yintercept could be 5. The negative slope here is steeperin general, less than 1.
Statement (2) is also insufficient. Such a slope is relatively steep, but it could result in positive or negative interceptsthe slope of the line doesn't determine the location of the line.
Taken together, the statements are sufficient. In (1), we learned that if the slope is less than 1, both intercepts are positive. Since the slope is less than 2, both intercepts must be positive. Choice (C) is correct.
Can you help ?
thanks proceed graphically and check the slope, 1) when the intercepts are in first quadrant, you will see the slope should be less than tan(135) i.e. less than 1 to satisfy the condition y>x intercept. (at 1 you will see x=y intercept) similarly, when in third quadrant slope should be greater than tan (135) i.e. 1 insufficient 2) insufficient both 1 and 2 slope less than 2 i.e. less than 1 hence both intercept are positive. hope this clarifies
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Re: In the xyplane, if line k has negative slope, is the [#permalink]
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15 Mar 2012, 09:15
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In the xyplane, if line k has negative slope, is the yintercept of line k positive?Equation of a line in point intercept form is \(y=mx+b\), where: \(m\) is the slope of the line and \(b\) is the yintercept of the line (the value of \(y\) for \(x=0\)). So, basically we are asked whether \(b>0\). (1) The xintercept of line k is less than the yintercept of line k > xintercept is value of \(x\) for \(y=0\), so it's \(\frac{b}{m}\). The statement says that: \(\frac{b}{m}<b\) > multiply by negative \(m\) and flip the sign of the inequality: \(b>bm\) > \(b(m+1)<0\). Now, in order \(b>0\) to be true \(m+1\) should be negative, so the question becomes: is \(m+1<0\)? > is \(m<1\). We don't know that. Not sufficient. (2) The slope of line k is less than 2. Insufficient on its own. (1)+(2) From (1) the question became: "is \(m<1\)?" and (2) says that \(m<2\). Sufficient. Answer: C.
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Re: In the xyplane, if line k has negative slope, is the [#permalink]
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In the xyplane, if line k has negative slope, is the [#permalink]
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11 Aug 2014, 05:13
Bunuel,
I dont understand
b/m<b > multiply by negative m and flip the sign of the inequality: b>bm > b(m+1)<0... can you explain?
IF b/m<b, then b<bm....b(m+1)>0...Can you explain how b(1+m) < 0?



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Re: In the xyplane, if line k has negative slope, is the [#permalink]
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12 Aug 2014, 08:30



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Re: In the xyplane, if line k has negative slope, is the [#permalink]
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13 Aug 2014, 07:49
b/m<b > If we multiply by negative m, we have to flip the sign as well as multiply by m on both sides. Isnt this correct?
If I multiply (left side equation) b/m by m => b/m*m => b If I multiply (right side equation) b by m => b*m If I flip the sign,
(Left side) b > b*m (right side) => b(1+m) > 0....Where did I go wrong? Please clarify my concept.



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Re: In the xyplane, if line k has negative slope, is the [#permalink]
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27 Aug 2015, 21:47
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Re: In the xyplane, if line k has negative slope, is the [#permalink]
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01 Nov 2015, 03:02
hi bunuel plz explain, why the sing of m is not considered here( at x intersept) y = mx +b , x = b/m, why its not x = b/m(taking m, negative slope)



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Re: In the xyplane, if line k has negative slope, is the [#permalink]
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01 Nov 2015, 09:07



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Re: In the xyplane, if line k has negative slope, is the [#permalink]
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04 Nov 2015, 08:19
Hi Bunuel, I have the same doubt as vipulgoel, however i couldn't understand your followup explanation. Since we know m is negative, shouldnt we take the sign into consideration ? Could you please explain what do you mean by "you do not substitute a variable say, x by x" ? Thanks.



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Re: In the xyplane, if line k has negative slope, is the [#permalink]
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04 Nov 2015, 09:50



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Re: In the xyplane, if line k has negative slope, is the [#permalink]
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06 Nov 2015, 22:08
hi, Let me try , y = mx+ c is a general form, irrespective of slope, first just write x intercept (without considering  ve slope), now as Bunuel did multiply with m(negative slope on both sides, that's how ve slope comes in picture)




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