Question

if two lines are perpendicular to each other then product of its slope is -1 find the slope of a line which is perpendicular to line AB if A is (3,0) and B is (0,2)

Answer 1

the line passes through (3,0) and (0,2)
therefore ots slope is -2/3 and thus the slope of the line perpendicular to this line is 3/2

Answer 2

$\large\sf\implies\:slope\: of \: points\: A\:(3,0) \:and\:B\:(0,2)$

$\large\sf\implies\:m\:=\frac{y_2-y_1}{x_2-x_1}$

$\large\sf\implies\:m\:=\frac{2-0}{0-3}$

$\large\sf\implies\:m\:=\frac{-2}{3}$

$\textsf{perpendicular slope is}$

$\large\bf\implies\:m_1\:×\: m_2\:=\:-1$

$\large\bf\implies\frac{\cancel{-}2}{3}\:×m_2\:=\cancel{-}1$

$\huge\sf\implies\:slope\:=\frac{3}{2}$