The above graphic has left out one possible case when considering Statement 2 here. One line certainly must have a negative y-intercept, and therefore a positive slope. The other line has a positive y-intercept. If that intercept is high, as in the diagram above, this line will have a negative slope. However, if the y-intercept is close to the origin (say at y=1), the line can have a positive slope. From S2 alone, we can't determine whether the product of the slopes will be positive or negative.
edit - sorry, I missed bigoyal's solution above, which is perfect.
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