The slope of $\displaystyle{y}=-{4}{x}-{5}\usepackage{cmbright}\Huge\$ is $\displaystyle-{4}\usepackage{cmbright}\Huge\$ . The slope of a perpendicular line is $\displaystyle\frac{{1}}{{4}}\usepackage{cmbright}\Huge\$ , the negative reciprocal of $\displaystyle-{4}\usepackage{cmbright}\Huge\$ . Its equation has the form $\displaystyle{y}=\frac{{1}}{{4}}{x}+{b}\usepackage{cmbright}\Huge\$ . To find b, substitute $\displaystyle{\left(-{2},{3}\right)}\usepackage{cmbright}\Huge\$ for x and y:

$\displaystyle{3}=\frac{{1}}{{4}}{\left(-{2}\right)}+{b}\usepackage{cmbright}\Huge\$ or $\displaystyle{3}=-\frac{{1}}{{2}}+{b}\usepackage{cmbright}\Huge\$ , so $\displaystyle\frac{{7}}{{2}}={b}\usepackage{cmbright}\Huge\$

The equation of the line is $\displaystyle{y}=\frac{{1}}{{4}}{x}+\frac{{7}}{{2}}\usepackage{cmbright}\Huge\$ .