Answer
$...\underline{\text{their slopes are equal}}$ and $\underline{\text{their y-intercepts}}$ are unequal;
$...\underline{\text{their slopes have a product of -1}}$.
Work Step by Step
The lines are parallel if their slopes are equal and the y-intercepts are unequal;
the lines are perpendicular if their slopes have a product of $-1$.