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In the xy-coordinate plane, line L and line K intersect at [#permalink]

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29 Nov 2006, 10:55

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In the xy-coordinate plane, line L and line K intersect at point (4,3). Is the product of their slopes negative?

(1) The product of the x-intercepts of lines L and K is positive

(2) The product of the y-intercepts of lines L and K is positive

How did you guys go about solving this?

For me...

??? (slope of L)*(slope of K) = negative number ???

--> the question is asking whether exactly one of the slopes is negative

(1) INSUFF both x intercepts could be positive or both negative
(2) INSUFF either y intercept of L is negative and for K positive or vice versa

I don't understand why together the statements are sufficient. Together, i come up with four possible scenarios but still not definite that one slope is negative.
_________________

When you take the information given in (1) and (2) together, you can surmise that there are 4 possibilities for these two lines, K and L.

1st possibility -> both x intercepts are +ve and both y intercepts are -ve In this case, both lines have to have +ve slope, and so the product of their slopes is positive.

2nd possibility -> both x intercepts are +ve and both y intercepts are +ve In this case, both lines have to have -ve slope, and so the product of their slopes is positive.

3rd possibility -> both x intercepts are -ve and both y intercepts are -ve In this case, both lines have to have -ve slope, and so the product of their slopes is positive.

4th possibility -> both x intercepts are -ve and both y intercepts are +ve In this case, both lines have to have +ve slope, and so the product of their slopes is positive.

So, we know for sure that the product of the slopes is positive. i.e., we have sufficient information to answer this question.

(1) If the products of both x-intercepts are -ve: L could have +ve slope and K -ve slope, or both +ve, or both -ve. In the 1st case, the products of the slopes are negative, while in the 2nd and 3rd they are positive. Insuff => B, C or E.

(2) Similar to (1). Insuff => C or E.

(1&2) The only possible case is that both L and K are -ve-sloped lines => the product of their slopes has to be -ve and the question has one answer => C.

in equation y=m*x+c
u find out Y intercept by putting X =0 and you get Y intercept is C
so same way you put y = 0 to get X intercept which will be -c/m

So if you have 2 lines.
product will be
(-c1/m1)*(-c2/m2) => c1c2/m1m2

Yogesh good thinking there.

I believe in this question... information that lines intersect at (4,3) is redundant.

another point I will add is... you will notice that

product of slopes = product of Y intercepts / product of X intercepts.

so when condition 1) and 2) are both given then product of slopes has to be positive.