Past exam of the mathematics course of the University of Cambridge / 2006 / ib / Paper 2 / 4F / ii / Solution

Factorization gives $y=x$ or $y=-x$. Each point can be joined to the origin by a straight segment lying on its own line. Two such segments join any pair of points, so the union is path-connected and hence connected. Alternatively it is the union of two connected lines with a common point.