Question

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?

Answer 1

The condition gives the two lines y = 2x and y = x/2, which are distinct lines through the origin. Two distinct lines through a point split the plane into 4 regions. Hence the graph divides the plane into 4 regions.