Points (2, 0) and (0, 3) lie on line k. What is the slope of the line that is perpendicular to k

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$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 2}}\quad ,&{{ 0}})\quad % (c,d) &({{ 0}}\quad ,&{{ 3}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{3-0}{0-2}\implies \boxed{\cfrac{-3}{2}}\\\\ -------------------------------\\\\$

$\bf \textit{perpendicular lines have, negative-reciprocal slope}\\\\ slope=\cfrac{a}{{{ b}}}\qquad negative\implies -\cfrac{a}{{{ b}}}\qquad reciprocal\implies - \cfrac{{{ b}}}{a}\\\\ -------------------------------\\\\ thus \\\\\\ \cfrac{-3}{2}\qquad negative\implies \cfrac{3}{2}\qquad reciprocal\implies \boxed{\cfrac{2}{3}}$

Points (2, 0) and (0, 3) lie on line k. What is the slope of the line that is perpendicular to k

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