In the xy-coordinate plane, line (l) and line (k) intersect : DS Archive
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# In the xy-coordinate plane, line (l) and line (k) intersect

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In the xy-coordinate plane, line (l) and line (k) intersect [#permalink]

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03 Dec 2007, 08:32
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In the xy-coordinate plane, line (l) and line (k) intersect at the point (4,3). Is the product of their slopes negative?

(1) The product of the x-intercepts of line (l) and (k) is positive
(2) The product of the y-intercepts of line (l) and (k) is negative

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03 Dec 2007, 09:20
I'd go for C.

From 1, we know that both x-intercepts are either positive or negative (only way to have a positive product). But we don't know about y, insuff.

From 2, we know y-intercepts are either positive or negative (because of the negative product) But we don't know about x, insuff.

Together, we know one of them must be positive and one negative, therefore, product of slope must be negative. C
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Re: DS: xy- coordinate plane [#permalink]

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04 Dec 2007, 11:54
alohagirl wrote:
In the xy-coordinate plane, line (l) and line (k) intersect at the point (4,3). Is the product of their slopes negative?

(1) The product of the x-intercepts of line (l) and (k) is positive
(2) The product of the y-intercepts of line (l) and (k) is negative

go with C.

Can't explain. I just drew a picture:)
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05 Dec 2007, 00:36
I think you assume that one must increase and the other must decrease. Anyway, you cannot know how many lines(L) and lines(K) have the quality the same as you mention only by that reason. Therefore, C is not sufficient. E is my choice
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Re: DS: xy- coordinate plane [#permalink]

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05 Dec 2007, 23:45
alohagirl wrote:
In the xy-coordinate plane, line (l) and line (k) intersect at the point (4,3). Is the product of their slopes negative?

(1) The product of the x-intercepts of line (l) and (k) is positive
(2) The product of the y-intercepts of line (l) and (k) is negative

Just draw lines.

Ul see that together the X's are both positive. and we have a negative y and positive y.

Using the drawings ul see we have one negative slope and one positive slope. Thus product is negative.
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Re: DS: xy- coordinate plane [#permalink]

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07 Dec 2007, 13:43
1
KUDOS
Line l, y = m1 x + c1
line k, y = m2 x + c2

1) Line l, x intercept = -c1/m1
Line K, x intercept = -c2/m2
So the product of intercepts c1 c2/m1 m2 is +ve

2) Line l, y intercept = c1
Line k, y intercept = c2
product is c1 c2 is -ve.

so from 1 & 2, we can conclude that m1 * m2 must be -ve.

So ans is C.
Re: DS: xy- coordinate plane   [#permalink] 07 Dec 2007, 13:43
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