To find the slope, solve for y: $\displaystyle{2}{y}={6}+{5}{x}\usepackage{cmbright}\Huge\$ , so $\displaystyle{y}={3}+\frac{{5}}{{2}}{x}\usepackage{cmbright}\Huge\$

The slope is $\displaystyle\frac{{5}}{{2}}\usepackage{cmbright}\Huge\$ . The slope of a perpendicular line is $\displaystyle-\frac{{2}}{{5}}\usepackage{cmbright}\Huge\$ . A perpendicular line has the form $\displaystyle{y}=-\frac{{2}}{{5}}{x}+{b}\usepackage{cmbright}\Huge\$ . To find b, substitute $\displaystyle{\left(-{10},{8}\right)}\usepackage{cmbright}\Huge\$ for x and y:

$\displaystyle{8}=-\frac{{2}}{{5}}{\left(-{10}\right)}+{b}\usepackage{cmbright}\Huge\$ , or $\displaystyle{8}={4}+{b}\usepackage{cmbright}\Huge\$ , so $\displaystyle{4}={b}\usepackage{cmbright}\Huge\$

This gives you the equation of the line: $\displaystyle{y}=-\frac{{2}}{{5}}{x}+{4}\usepackage{cmbright}\Huge\$