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The OA here is C. The easiest way to solve this problem is by drawing a graph. When the question asks whether the product of the slope is negative, what the question is really asking is whether one line is going upward and the second line is going downward through the intersection of (4,3):
1) the product of the x-intercept is positive. this means that both lines are touching the x-axes in quadrant 1. On the one hand, 1 line could be going upward through (4,3), while the second line goes downward through (4,3). On the other hand, both lines could be going upward through the point (4,3) ---not suff.
2) product of the y intercepts is negative. On the one hand, both lines could be going upward through the point (4,3), but 1 of the lines has the y intercept in the negative side, while the second line could still be going upward from just above the origin. On the other hand, 1 line could be going upward from the negative y-intercept, while the second line could be going downward from above the y-intercept 4. So not suff.
(1&2) when both the lines have a positive x-intercept, while one of the y-intercept is negative while the second is positive, then obviously, 1 is going upward, and the second is going downward, so the product of the slope is negative, and therefore Suff.