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.
