In the xy-plane, line k is a line that does not pass through the origin. Which of the following statements provide(s) sufﬁcient additional information to determine whether the slope of line k is negative?

Indicate all such statements.

A. The x-intercept of line k is twice the y-intercept of line k.
B. The product of the x-intercept and the y-intercept of line k is positive.
C. Line k passes through the points and where (a, b) (r, s), where (a − r)(b − s) < 0.

Here what about the following case? I do not understand how option a is sufficient or even necessary to determine if the slope is negative.

Thanks for your response, but two lines does not really matter in this case, because all I am trying to explain is an example. Both of the above lines can have x intercept twice of y intercept but still have a positive slope.

OK. There is a problem with the diagram though. If the x intercept is twice the y-intercept, then x and y must both be positive or be negative. In your diagram, one of them is positive and the other is negative, which fails the condition as a result.