Consider the set of all points (x, y) in the coordinate plane for which one of the coordinates is exactly twice the other. if we were to plot all such points, into how many regions would the resulting graph split up the plane?

If x is twice that of y, then x = 2y forming one possible equation. This plots a straight line through the points
(0,0)
(2,1)
(4,2)
etc etc. Basically whatever y is, double it to get x

Another possible equation is y = 2x which is a straight line through the points
(0,0)
(1,2)
(2,4)
etc. The flip of the other list of points above. 

Because it is not clear which coordinate is doubled, we can't say for sure which equation we'll pick. However, we only pick one equation. This one equation produces only one line that splits the xy plane into two parts. So there are 2 regions. 

No i refuse to tell you the answer but the estimate is 10