The slope of $\displaystyle{y}=-\frac{{1}}{{4}}{x}-{2}\usepackage{cmbright}\Huge\$ is $\displaystyle-\frac{{1}}{{4}}\usepackage{cmbright}\Huge\$ . The slope of a perpendicular line is 4, the negative reciprocal of $\displaystyle-\frac{{1}}{{4}}\usepackage{cmbright}\Huge\$ . Its equation has the form $\displaystyle{y}={4}{x}+{b}\usepackage{cmbright}\Huge\$ . To find b, substitute $\displaystyle{\left(-{2},-{3}\right)}\usepackage{cmbright}\Huge\$ for x and y:

$\displaystyle-{3}={4}{\left(-{2}\right)}+{b}\usepackage{cmbright}\Huge\$ or $\displaystyle-{3}=-{8}+{b}\usepackage{cmbright}\Huge\$ , so $\displaystyle{5}={b}\usepackage{cmbright}\Huge\$

The equation of the line is $\displaystyle{y}={4}{x}+{5}\usepackage{cmbright}\Huge\$ .