Parallel, Perpendicular, or Intersecting Lines

Identify the relationship

For each pair of lines, decide whether they are parallel, perpendicular, or intersecting. The key is to compare their slopes when equations are given, or to use the visual information if a graph or diagram is shown.

1. Compare slopes

• Parallel lines have the same slope and different intercepts.
• Perpendicular lines have slopes that are negative reciprocals of each other. For example, slopes (m) and (-\frac{1}{m}).
• Intersecting lines are neither parallel nor perpendicular. They cross at one point, but their slopes do not match the parallel or perpendicular pattern.

2. Simplify carefully

If the line equations are not already in slope form, rewrite them so the slope is easy to read. Simplify fractions and signs before comparing.

3. Use the graph if needed

If the lines are shown on a coordinate plane:

• Parallel lines keep the same direction.
• Perpendicular lines meet at a right angle.
• Intersecting lines cross, but not necessarily at 90°.

4. Check your answer

After classifying the pair, verify that your slope comparison or visual reasoning matches your conclusion. If the slopes are equal, the lines are parallel; if the slopes multiply to (-1), they are perpendicular; otherwise, they are intersecting.