the slope of a line who is perpendicular to another, is the negative reciprocal slope of that line, that is, if a line has slope say a/b, then
[tex]\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{a}{b}\\\\
slope=\cfrac{a}{{{ b}}}\qquad negative\implies -\cfrac{a}{{{ b}}}\qquad reciprocal\implies - \cfrac{{{ b}}}{a}\\\\
-------------------------------\\\\
slope=-2\qquad negative\implies +2\qquad reciprocal\implies \cfrac{1}{2}[/tex]
so.. what is the equation of a line whose slope is 1/2 and passes through (2,5)?
[tex]\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ 2}}\quad ,&{{ 5}})\quad
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{1}{2}
\\\\\\
% point-slope intercept
y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-5=\cfrac{1}{2}(x-2)\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
y-5=\cfrac{1}{2}x-1\implies y=\cfrac{1}{2}x+4[/tex]
