Question 471982
a) If the line goes through the points (2z,0) and (0,z) then the slope is z/(-2z) = -2. This works for all nonzero z, so a) works.


b) Let (x,0) and (0,y) denote the x- and y-intercepts. The slope is obviously -y/x. Given that xy is positive, then x,y are either both positive or both negative, and the quotient y/x is also positive. However the slope of k is -y/x so this is negative, so b) works.


c) The slope of the line k is (b-s)/(a-r) (the order of which we choose the points does not matter). Since (a-r)(b-s) < 0, it follows that exactly one of a-r or b-s is negative, and the slope of k is also negative (similar scenario as part b)).


Hence, all three statements work.