hi, i saw this problem, earlier and try to say something
line L=y=kx+b, and
line K=y=k1*x+b1,
we need to estimate does k*k1<0
(1)if y=0, then for line L. kx=-b,x=-b/k and for line K k1*x=-b1. x=-b1/k1 and the product of x interceps is +ve
(-b/k)*(-b1/k1)>0
(b*b1)/(k*k1)<0 it possible in two cases
b*b1>0 and k*k1<0 or
b*b1<0 and k*k1>0 as we don`t know for sure the sign st 1 is insuff
(2)if x=0 then for line L y=b and for line K y=b1
and given that b*b1<0, but nothing is said about k and k1 also insuff
both
as b*b1>0 from 1 st it follows that k*k1<0
so suff my answer is C
P,S don`t know for what purpose we need point (4,3)

the easiest way to solve this q. is to start from the question itself and to fix x,y coordinates for L and K to prove the product of their slopes can be negative, positive or both.
st(1) is not Sufficient alone as it fixes only x coordinate for the intercepts (y=0) and can be positive for their products on the LHS from the origin too;
st(2) is not Sufficient alone as well, it can be below y=3 but still negative with another coordinate of y below 0;
combined st(1&2) we get the fixed ceilings for x and y coordinates crossing the point (4,3) and exclude x on the LHS (only RHS may exist) Sufficient;

c

Dean Jones wrote:Hi Freinds,

I am having difficulty in solving the below mentioned problem.Please help.

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.

OA after some discussion.

Regards
Deano.

OA is C

I

Dean Jones wrote:Hi Freinds,

I am having difficulty in solving the below mentioned problem.Please help.

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.

OA after some discussion.

Regards
Deano.

Don't solve. Draw.

Statement 1: The product of the x-intercepts of line L and K is positive.
K has a negative x-intercept, L has a negative x-intercept, the product of the slopes is positive:


K has a positive x-intercept, L has a positive x-intercept, the product of the slopes is negative:

Insufficient.

Statement 2: The product of the y-intercepts of line L and k is negative.
K has a negative y-intercept, L has a positive y-intercept, the product of the slopes is negative:


K has a negative y-intercept, L has a positive y-intercept, the product of the slopes is positive:

Insufficient.

Statements 1 and 2 combined:
Statement 1 requires that both x-intercepts be negative or that both be positive (so that their product is positive).
If both x-intercepts are negative, then both y-intercepts must be positive, which does not satisfy statement 2:


Thus, both x-intercepts must be positive.
Statement 2 requires that one of the y-intercepts be positive, the other negative.
A positive x-intercept and a positive y-intercept yields a negative slope.
A positive x-intercept and a negative y-intercept yields a positive slope.
See below:

Thus, the product of the slopes must be negative.
Sufficient.

The correct answer is C.

Dean Jones wrote:Hi Freinds,

I am having difficulty in solving the below mentioned problem.Please help.

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.

OA after some discussion.

Regards
Deano.

Is this true for all lines. If
(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.
Then: the product of their slopes negative?