In the xy plane, line l and line k intersect at the point (4,3). Is the product of their slopes negative?
1) The product of x intercepts of lines l and k is positive.
2) The product of y intercepts of lines l and k is negative.
from the main statement we know that the lines pass through the first quadrant
then what? I think is easier to solve if you draw a cartesian plane
from (1) the intercepts are either both positive or both negative
in that case if both -ve, then slopes would be positive
in that case if both +ve, then impossible to know, if they are at the right of point (4,3) would be -ve, at the left of that point positive, but one can at the right, the other one at the left, so I'd say (1) is insuff.
from (2) product of y intercepts are negative, so one of the intercepts is bigger than one and the other one smaller
for the one has negative intercept slope is always +ve, but we don't know for sure for the one that has +ve intercept, it depends if is lower or higher than point (4,3)
taking (1) and (2)
intercepts of x must be both positive,
the line with -ve y intercept would have a positive slope
the line with +ve y intercept would have a negative slope
=> I would say the answer is C
sorry, too wordy, a little graph would work much better