To find the slope, solve for y: $\displaystyle{8}{y}={16}-{6}{x}\usepackage{cmbright}\Huge\$ , so $\displaystyle{y}={2}-\frac{{6}}{{8}}{x}\usepackage{cmbright}\Huge\$ or $\displaystyle{y}=-\frac{{3}}{{4}}{x}+{2}\usepackage{cmbright}\Huge\$

The slope is $\displaystyle-\frac{{3}}{{4}}\usepackage{cmbright}\Huge\$ . The slope of a parallel line is $\displaystyle-\frac{{3}}{{4}}\usepackage{cmbright}\Huge\$ . A parallel line has the form $\displaystyle{y}=-\frac{{3}}{{4}}{x}+{b}\usepackage{cmbright}\Huge\$ . To find b, substitute $\displaystyle{\left({12},-{9}\right)}\usepackage{cmbright}\Huge\$ for x and y:

$\displaystyle-{9}=-\frac{{3}}{{4}}{\left({12}\right)}+{b}\usepackage{cmbright}\Huge\$ , or $\displaystyle-{9}=-{9}+{b}\usepackage{cmbright}\Huge\$ , so $\displaystyle{0}={b}\usepackage{cmbright}\Huge\$

This gives you the equation of the line: $\displaystyle{y}=-\frac{{3}}{{4}}{x}\usepackage{cmbright}\Huge\$