Parallel lines are lines that will go on and on forever without ever intersecting. This is because they have the same slope! If you have two linear equations that have the same slope but different y-intercepts, then those lines are parallel to one another!
Perpendicular lines intersect at right angles to one another. To figure out if two equations are perpendicular, take a look at their slopes. The slopes of perpendicular lines are opposite reciprocals of each other. Their product is -1! Watch this tutorial and see how to determine if two equations are perpendicular.
Got a diagram of a transversal intersecting parallel lines? Trying to figure out all the angle measurements? Take a look at this tutorial, and you'll see how find all the missing angle measurements by identifying vertical, corresponding, adjacent, and alternate exterior angles!