Exercise 3 Page 177

Before we think about how you can recognize when lines are parallel or perpendicular, let's look at a graph with an example of each.

In this example, the red and blue lines are parallel and the green line is perpendicular to both of them. Visually, we can see that lines are parallel because they will never intersect, they will continue on forever without ever crossing paths. Algebraically, we can know that lines are parallel because they have the same slope. In our example, we have: Similarly, we can tell that lines are perpendicular when looking at them because when they intersect, it is at a perfect $90^{\circ }$ angle. Algebraically, we can know that lines are perpendicular because their slopes are negative reciprocals. On the graph, we have: