Line E passes through the points (2, 3) and (4, -3). What is the slope of a line perpendicular to line E?

1 answer:

7 0

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ 2 &,& 3~) 
% (c,d)
&&(~ 4 &,& -3~)
\end{array}
\\\\\\
% slope = m
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-3-3}{4-2}\implies \cfrac{-6}{2}\implies \cfrac{-3}{1}$

now, a line perpendicular to that one, will have a "negative reciprocal" slope, thus

$\bf \textit{perpendicular, negative-reciprocal slope for}\quad \cfrac{-3}{1}\\\\
negative\implies +\cfrac{3}{ 1}\qquad reciprocal\implies +\cfrac{ 1}{3}\implies \cfrac{1}{3}$

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