Question

What is the slope of the line passing through the points (2a, 3b) and (2b, 3a)?​

Answer 1

$Let \: A(x_{1} , y_{1}) = ( 2a , 3b) \: and \\ B(x_{2} , y_{2}) = ( 2b , 3a)$

$Slope \: of \: a \: line \: AB \\= \frac{y_{2} - y_{1}}{x_{2} - x_{1} } \\= \frac{3a - 3b}{2b-2a} \\= \frac{3(a-b)}{2(b-a)} \\ = \frac{ 3\cancel {(a-b)}}{-2\cancel {(a-b)} } \\= \frac{-3}{2}$

Therefore.,

$\red{ Slope \: of \: the \: line \: AB} \green { = \frac{-3}{2} }$

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