#### Answer

$...\text{ are perpendicular if } a = -\frac{1}{2}$.

#### Work Step by Step

RECALL:
(i) Non-vertical lines are parallel if they have equal slopes.
(ii) Non-vertical and non-horizontal lines are perpendicular if their slopes have a product of −1
Thus, for the given lines to be perpendicular, the product of their slopes must be $-1$,
For this to happen, the value of $a$ must be $-\frac{1}{2}$.