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In the xy-plane, line k is a line that does not pass throug

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In the xy-plane, line k is a line that does not pass throug [#permalink] New post 18 Jan 2016, 15:26
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In the xy-plane, 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 x-intercept of line k is twice the y-intercept of line k.
B. The product of the x-intercept and the y-intercept of line k is positive.
C. Line k passes through the points and where (a, b) (r, s), (a − r)(b − s) < 0.

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Question: 11
Page: 340
Difficulty: medium
[Reveal] Spoiler: OA

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Re: In the xy-plane, line k is a line that does not pass throug [#permalink] New post 18 Jan 2016, 15:32
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Solution

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You 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 x-intercept is twice the y-intercept, 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 x-intercept and the y-intercept 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 \(\frac{b-s}{a-r}\)
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 \(\frac{b-s}{a-r}\), 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 xy-plane, line k is a line that does not pass throug [#permalink] New post 23 Dec 2016, 05:12
"Choice A states that the x-intercept is twice the y-intercept, 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 cor-ordiante?
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Re: In the xy-plane, line k is a line that does not pass throug [#permalink] New post 23 Dec 2016, 06:07
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malihanajia wrote:
"Choice A states that the x-intercept is twice the y-intercept, 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 cor-ordiante?



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 xy-plane, line k is a line that does not pass throug   [#permalink] 23 Dec 2016, 06:07
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