Hi,
Let line l be y = ax+b, where slope is a and y-intercept is b
and line k be y = cx+d where slope is c and y-intercept is d
Product of slopes is a.c
From(1):
X-intercept of l is (-b/a)
X-intercept of k is (-d/c)
Product is bd/ac > 0
Not sufficient
From(2):
Product of y-intercepts is b.d<0
Not sufficient

Both (1)&(2): bd/ac> 0 and bd<0. So ac must be negative
Sufficient

Hence, C

Think of the possibilities for 2 lines intersecting.

They could both be the same vertical line. They could both be the same horizontal line. They could both tilt to the right (positive slopes). They could both tilt to the left (negative slopes). Or one could tilt to the right and the other could tilt to the left.

To know what the product of the slopes will be, we need to get a better sense of how these lines appear on the graph.

(1) If the product is positive, this could mean that both x-intercepts are positive, or both are negative. This is not enough information to determine the slope.

(2) If the product is negative, this means that one y-intercept is negative, and the other is positive. Again, this is not enough information.

If we combine however, we have enough. Both lines will have to have positive x-intercepts for one of them to have a negative y-intercept. They will cross each other like a "X" at (4,3), and the slopes will have opposite signs.

IMO: C

So the point (4,3) has no significance?

It's not necessary.