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In the xyplane, line k is a line that does not pass throug [#permalink]
18 Jan 2016, 15:26
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In the xyplane, line k is a line that does \(not\) pass through the origin. Which of the following statements \(individually\) provide(s) sufﬁcient additional information to determine whether the slope of line k is negative? Indicate all such statements. A. The xintercept of line k is twice the yintercept of line k. B. The product of the xintercept and the yintercept of line k is positive. C. Line k passes through the points and where (a, b) (r, s), where (a − r)(b − s) < 0. Practice Questions Question: 11 Page: 340 Difficulty: medium
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Re: In the xyplane, line k is a line that does not pass throug [#permalink]
18 Jan 2016, 15:32
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SolutionYou can use this fact to examine the information given in the first two statements. Remember that you need to evaluate each statement by itself. Choice A states that the xintercept is twice the yintercept, so you can conclude that both intercepts have the same sign, and thus the slope of line k is negative. So the information in Choice A is sufficient to determine that the slope of line k is negative. Choice B states that the product of the xintercept and the yintercept is positive. You know that the product of two numbers is positive if both factors have the same sign. So this information is also sufficient to determine that the slope of line k is negative. Choice C, it is helpful to recall the definition of the slope of a line passing through two given points. You may remember it as “rise over run.” If the two points are (a, b) and (r, s), then the slope is \(\frac{bs}{ar}\) Choice C states that the product of the quantities (a−r) and (b−s) is negative. Note that these are the denominator and the numerator, respectively, of \(\frac{bs}{ar}\), the slope of line k. So you can conclude that (a−r) and (b−s) have a−r opposite signs and the slope of line k is negative. The information in Choice C is sufficient to determine that the slope of line k is negative. So each of the three statements individually provides sufficient information to determine whether the slope of line k is negative. The correct answer are \(A, B, and C\).
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Re: In the xyplane, line k is a line that does not pass throug [#permalink]
23 Dec 2016, 05:12
"Choice A states that the xintercept is twice the yintercept, so you can conclude that both intercepts have the same sign, and thus the slope of line k is negative." How can you assure that slope of line k is negative?? please can you explain it with let the x and y corordiante?



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Re: In the xyplane, line k is a line that does not pass throug [#permalink]
23 Dec 2016, 06:07
malihanajia wrote: "Choice A states that the xintercept is twice the yintercept, so you can conclude that both intercepts have the same sign, and thus the slope of line k is negative." How can you assure that slope of line k is negative?? please can you explain it with let the x and y corordiante? This is actually a tricky one! What you are thinking about is x intercept = 4 and y intercept = 2. However \(4 \neq 2*2\) hence even the first statement is sufficient for a ve slope line K.
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Re: In the xyplane, line k is a line that does not pass throug [#permalink]
22 May 2020, 14:00
Carcass I didnt understand choice A Carcass wrote: SolutionYou can use this fact to examine the information given in the first two statements. Remember that you need to evaluate each statement by itself. Choice A states that the xintercept is twice the yintercept, so you can conclude that both intercepts have the same sign, and thus the slope of line k is negative. So the information in Choice A is sufficient to determine that the slope of line k is negative. Choice B states that the product of the xintercept and the yintercept is positive. You know that the product of two numbers is positive if both factors have the same sign. So this information is also sufficient to determine that the slope of line k is negative. Choice C, it is helpful to recall the definition of the slope of a line passing through two given points. You may remember it as “rise over run.” If the two points are (a, b) and (r, s), then the slope is \(\frac{bs}{ar}\) Choice C states that the product of the quantities (a−r) and (b−s) is negative. Note that these are the denominator and the numerator, respectively, of \(\frac{bs}{ar}\), the slope of line k. So you can conclude that (a−r) and (b−s) have a−r opposite signs and the slope of line k is negative. The information in Choice C is sufficient to determine that the slope of line k is negative. So each of the three statements individually provides sufficient information to determine whether the slope of line k is negative. The correct answer are \(A, B, and C\).
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Re: In the xyplane, line k is a line that does not pass throug [#permalink]
22 May 2020, 15:00
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No matter value you consider for x then y is 1/2 of x Of course, if x is 4 y must be 2 because Y cannot be for instance 2 because 2 is NOT 1/2 of 4 Hope now is more clear
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Re: In the xyplane, line k is a line that does not pass throug [#permalink]
21 Jun 2020, 00:26
For option A, if the X and Y intercepts are 0, then X intercept will indeed be twice that of Y intercept. So couldn't a line have a positive slope like y = x and still satisfy the A condition?



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Re: In the xyplane, line k is a line that does not pass throug [#permalink]
21 Jun 2020, 05:16
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Zohair123 wrote: For option A, if the X and Y intercepts are 0, then X intercept will indeed be twice that of Y intercept. So couldn't a line have a positive slope like y = x and still satisfy the A condition? Good idea, but the x and yintercepts cannot both be 0, since the question explicitly tells us that " line k does NOT pass through the origin"
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Re: In the xyplane, line k is a line that does not pass throug [#permalink]
21 Jun 2020, 23:12
GreenlightTestPrep wrote: Zohair123 wrote: For option A, if the X and Y intercepts are 0, then X intercept will indeed be twice that of Y intercept. So couldn't a line have a positive slope like y = x and still satisfy the A condition? Good idea, but the x and yintercepts cannot both be 0, since the question explicitly tells us that " line k does NOT pass through the origin" That's a very valid point, thank you. I guess this scenario is one of the main reasons to include the "not origin" clause in the question.




Re: In the xyplane, line k is a line that does not pass throug
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21 Jun 2020, 23:12





