To tell whether two lines are parallel or perpendicular, you need to know how to find the slope of a line. (The slope of a line is a measurement of what direction it goes in.) Usually, when you're given the equation of a line, it will look like y = 5x − 3. In this case, the slope of the line is 5. In general, if you have y by itself, then the slope is the number in front of the x. The number being added or subtracted doesn't matter.
Once you have the slopes of the two lines, you just need to apply the general rule. If two lines have the same slope, then they're parallel. (This makes sense, since then they go in the same direction.) To check if two lines are perpendicular, you need to multiply the two slopes. If you get the answer of −1, then they're perpendicular. It's okay if two lines are neither parallel nor perpendicular.
Sometimes, there won't be an x. In that case, the line is horizontal. For example, the line y = 5 is horizontal. Any two horizontal lines are parallel, so y = 5 is parallel to y = −2. Other times, there's no y, as in the line x = 2. In that case, the line is vertical. Any two vertical lines are also parallel. Also, any vertical line is perpendicular to any horizontal line. Finally, if one line is horizontal or vertical and the other is normal (that is, it has both an x and a y in it), then the lines are neither parallel nor perpendicular.