Correct. Graph $\displaystyle{y}=-{x}\usepackage{cmbright}\Huge\$ . Test an ordered pair on either side of the boundary line.

For $\displaystyle{\left({0},{1}\right)}\usepackage{cmbright}\Huge\$ : $\displaystyle{1}>{0}\usepackage{cmbright}\Huge\$ TRUE; For $\displaystyle{\left({0},-{1}\right)}\usepackage{cmbright}\Huge\$ : $\displaystyle-{1}>{0}\usepackage{cmbright}\Huge\$ FALSE

The region that includes $\displaystyle{\left({0},{1}\right)}\usepackage{cmbright}\Huge\$ is shaded. This includes only parts of Quadrants II and IV, but all of Quadrant I.