We can determine if two straight lines are either parallel or they are perpendicular by checking their slopes.

y₁ = m₁x + b₁  (equation for line 1)

y₂ = m₂x + b₂ (equation for line 2)

For two lines to be parallel their slopes have to be same. That is, m₁ = m₂

If, two straight lines are perpendicular their slopes have to be reciprocal and negative. That is, m₁ = -1/m₂

Hope this answers your question.

Two straight lines are parallel if they have the same slope.

Two straight lines are perpendicular if the product of their slopes is -1.

So, if you know how to find slope, you can get the answer.