You found the slope of a line that is perpendicular to $\displaystyle{y}={2}{x}-{4}\usepackage{cmbright}\Huge\$ , not parallel. Parallel lines have the same slope but different y-intercepts. So to find the slope of a parallel line you must find the slope of $\displaystyle{y}={2}{x}-{4}\usepackage{cmbright}\Huge\$ .