If x and y are negative integers and x – y = 1,
what is the least possible value for xy?

X=y+1
Least possible value for y(y+1)? Well, it appears for y halfway between the roots (you know what a parabola is, don't you?). That y is -0.5, so let's calculate -0.5*0.5, which is -0.25.
The least possible value is
Well, not really :)) The two values must be both negative, so we can't take one of them to be 0.5! As we lower the values, however, the product grows, reaching 0 when x=0 and y=-1, and further increasing as x and y lower. Thus, we would actually take x=0 and y=-1.