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Parallel lines have the same slopes which means that they have the same slope. The slope is determine by the coefficient in front of the $x$-term. $y=ax+2y=3x−8 $ Thus, $a=3$ will make the lines parallel.

b

$m_{1}⋅m_{2}=-1$

$a⋅3=-1$

DivEqn$LHS/3=RHS/3$

$a=3-1 $

MoveNegNumToFracPut minus sign in front of fraction

$a=-31 $

The slope $a$ must be equal to $-31 $ if the lines are perpendicular.