first off, what is the slope of say y = -1/2x+3? well, let's take a peek
[tex]\bf y=\stackrel{slope}{-\cfrac{1}{2}}x+3[/tex]
well, then, a line perpendicular to that line, will have a slope that is negative reciprocal to that one, so if the slope of that graph is -1/2, then
[tex]\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad -\cfrac{1}{2}\\\\
slope=-\cfrac{1}{{{ 2}}}\qquad negative\implies +\cfrac{1}{{{ 2}}}\qquad reciprocal\implies + \cfrac{{{ 2}}}{1}\implies 2[/tex]
so, we're really looking for the equation of a line whose slope is 2, and runs through -7, 2.
[tex]\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ -7}}\quad ,&{{ 2}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 2
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-2=2[x-(-7)]
\\\\\\
y-2=2(x+7)\implies y-2=2x+14\implies y=2x+16[/tex]
