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1) We are given that the product of the two point's x coordinates is positive. This doesn't tell us much because the two y coordinates could be positive yielding a positive slope or the two y coordinates could be negative yielding a negative slope.
2) Here we are given that the product of the y coordinates are negative. But again this doesn't tell us whether the x coordinates are positive or negative which could yield either a positive or negative slope.
3) Together we know that the X coordinates are positive and the Y coordinates are negative. Hence we can determine that the slope is indeed negative.