If slope $\displaystyle{m}=\frac{{{y}_{{2}}-{y}_{{1}}}}{{{x}_{{2}}-{x}_{{1}}}}={0}\usepackage{cmbright}\Huge\$ , then $\displaystyle{y}_{{2}}-{y}_{{1}}={0}\usepackage{cmbright}\Huge\$ , or $\displaystyle{y}_{{2}}={y}_{{1}}\usepackage{cmbright}\Huge\$ . That is, all y-coordinates have the same value. All the points on a horizontal line have the same y-coordinate.