The slope of $\displaystyle{y}={3}{x}-{5}\usepackage{cmbright}\Huge\$ is 3. The slope of a perpendicular line is $\displaystyle-\frac{{1}}{{3}}\usepackage{cmbright}\Huge\$ , the negative reciprocal of 3. Its equation has the form $\displaystyle{y}=-\frac{{1}}{{3}}{x}+{b}\usepackage{cmbright}\Huge\$ . To find b, substitute (6, 4) for x and y:

$\displaystyle{4}=-\frac{{1}}{{3}}{\left({6}\right)}+{b}\usepackage{cmbright}\Huge\$ , or $\displaystyle{4}=-{2}+{b}\usepackage{cmbright}\Huge\$ , so $\displaystyle{6}={b}\usepackage{cmbright}\Huge\$

This gives the equation of the line: $\displaystyle{y}=-\frac{{1}}{{3}}{x}+{6}\usepackage{cmbright}\Huge\$