Plot the graph of $4 y - 2 x = 10$ and $- 6 y - 6 = - 3 x$ .
Are these lines parallel, perpendicular or neither?

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Solution

$L_{1} = 4 y - 2 x = 10$
$= 4 y = 2 x + 10$
$y = \frac{x}{2} + \frac{10}{4}$
$L_{2} = - 6 y - 6 = - 3 x$
$= 6 y = 3 x - 6$
$y = \frac{x}{2} - 1$
For two lines:
$y = m_{1} x + c_{1}$
$y = m_{2} x + c_{2}$
Lines are parallel if
$m_{1} = m_{2}$
In this equation, $m_{1} = m_{2}$
Therefore lines are parallel

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