Substitute the slope $\displaystyle\frac{{3}}{{2}}\usepackage{cmbright}\Huge\$ into $\displaystyle{y}={m}{x}+{b}\usepackage{cmbright}\Huge\$ : $\displaystyle{y}=\frac{{3}}{{2}}{x}+{b}\usepackage{cmbright}\Huge\$

Substitute the coordinates of the point $\displaystyle{\left(-{2},-{4}\right)}\usepackage{cmbright}\Huge\$ for x and y: $\displaystyle-{4}=\frac{{3}}{{2}}{\left(-{2}\right)}+{b}\usepackage{cmbright}\Huge\$

Solve for b: $\displaystyle-{4}=-{3}+{b}\usepackage{cmbright}\Huge\$ , so $\displaystyle-{1}={b}\usepackage{cmbright}\Huge\$

Rewrite $\displaystyle{y}={m}{x}+{b}\usepackage{cmbright}\Huge\$ with $\displaystyle{m}=\frac{{3}}{{2}}\usepackage{cmbright}\Huge\$ and $\displaystyle{b}=-{1}\usepackage{cmbright}\Huge\$ : $\displaystyle{y}=\frac{{3}}{{2}}{x}-{1}\usepackage{cmbright}\Huge\$