tanyajoseph 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 lines l and k is positive
2. The product of the yintercepts of lines l and k is negative.

My answer would be [C], sufficient together.

let the following equations represent the lines l and k:

y = m1.x + b1 ........... (l)
y = m2.x + b2 ........... (k)

where m1 and m2 are slopes and b1 and b2 are y intercepts of line l and k, respectively.

The question can then be rephrased as m1.m2 < 0?

x intercepts will be -b1/m1 and -b2/m2 respectively.

Statement (1) gives us:
(-b1/m1).(-b2/m2) > 0
(-1).(b1/m1).(-1).(b2/m2) > 0
(b1/m1)(b2/m2) > 0 .................. (c)

This is not sufficient to determine if m1.m2 < 0 or not.

Statement (2) gives us:
b1.b2 < 0, which means b1 and b2 are of opposite signs, one is negative and the other is positive.

This is not sufficient on itself to determine if m1.m2 < 0 or not.

Taken together, equation (c) would be true, only if m1 and m2 are of opposite signs. Hence m1.m2 < 0.

Answer [C].

Note: the point (4,3) doesn't serve any purpose whatsoever in my explanation. Not sure if thats ok or not.

I dont really understnd

tanyajoseph wrote:I dont really understnd

Whats your question?