The question asks about the slope of a line and whether the slope will be positive or negative depending on the x- and y-intercepts. What about when the x- and y-intercepts are both 0 (i.e. the line goes through the origin). Their product, 0, is neither positive nor negative. Additionally, the slope of that line could either be positive or negative (y=x or y=-x as examples). Why is the answer to this question not, D?
Kindly share the picture of the question too.
Because here the options clearly specify that:
For A: product is negative
For B: product is positive
So, you are not supposed to consider the case where both are 0, as that is not useful for any of the options.
Now, if you sketch the different types of lines, where the product is positive and negative, you will find that the slope is positive, if the product is negative (option A) and the slope is negative, if the product is positive (option B)
Thus, option A is the correct asnwer.