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In the xy-coordinate plane, line (l) and line (k) intersect

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Intern
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In the xy-coordinate plane, line (l) and line (k) intersect [#permalink] New post 03 Dec 2007, 08:32
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A
B
C
D
E

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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

Please help explain to me this question
Senior Manager
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 [#permalink] New post 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] New post 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

Please help explain to me this question


go with C.

Can't explain. I just drew a picture:)
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 [#permalink] New post 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] New post 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

Please help explain to me this question



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] New post 07 Dec 2007, 13:43
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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

so no conclusions can be made about the product of slopes.

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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