Find the slope using the given points: $\displaystyle\frac{{{2}-{0}}}{{-{2}-{0}}}=\frac{{2}}{{-{{2}}}}=-{1}\usepackage{cmbright}\Huge\$

Substitute the slope (m) into $\displaystyle{y}={m}{x}+{b}\usepackage{cmbright}\Huge\$ : $\displaystyle{y}=-{1}{x}+{b}\usepackage{cmbright}\Huge\$ , or $\displaystyle{y}=-{x}+{b}\usepackage{cmbright}\Huge\$

Since the line passes through the origin (0, 0), the y-intercept of the line is 0. Substitute 0 for b and rewrite the equation as $\displaystyle{y}=-{x}+{0}\usepackage{cmbright}\Huge\$ , or $\displaystyle{y}=-{x}\usepackage{cmbright}\Huge\$ .