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Picture a point in the first quadrant (+,+) doesn't matter where exactly
1. If the product of the X intercepts is positive then they both cross the X axis on the same side of the Y axis (ie, the intercepts are either both positive or both negative). Both lines could cross on the positive side and have opposite slopes (or the same type of slope).
2. this means the lines cross the Y axis on different sides of the X axis. They could cross on opposite sides with the same sign slope (just different degrees of slope) or different signed slopes.
now taken TOGETHER. They have to cross the X axis on the positive side, but cross the Y axis on different sides of the X axis. For this to be possible they MUST have different signed slopes. One negative and one positive.
Answer is C.
I know this is maybe the worst explanation ever given. I didn't write anything down or chart it out, I just pictured the situation and went from there. Try sketching it out and seeing for yourself.