The slope of $\displaystyle{y}=-\frac{{1}}{{2}}{x}+{3}\usepackage{cmbright}\Huge\$ is $\displaystyle-\frac{{1}}{{2}}\usepackage{cmbright}\Huge\$ . The slope of a perpendicular line is 2, the negative reciprocal of $\displaystyle-\frac{{1}}{{2}}\usepackage{cmbright}\Huge\$ . Its equation has the form $\displaystyle{y}={2}{x}+{b}\usepackage{cmbright}\Huge\$ . To find b, substitute (2, 7) for x and y:

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

This gives the equation of the line: $\displaystyle{y}={2}{x}+{3}\usepackage{cmbright}\Huge\$