Show that the lines $x + 2 y = 0, 2 x + 4 y = 9$ are parallel.

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Solution

First line $x + 2 y = 0$

Slope $m_{1} = \frac{- c o e f f i c i e n t o f x}{c o e f f i c i e n t o f y} = \frac{- 1}{2}$

Second line is $2 x + 4 y = 9$

Slope $m_{2} = \frac{- c o e f f i c i e n t o f x}{c o e f f i c i e n t o f y} = \frac{- 2}{4} = \frac{- 1}{2}$

$∴ m_{1} = m_{2} = \frac{- 1}{2}$

$∴$ Given lines are parallel.

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