To find the best solution.
Graphs can be used to compare two different equations. For example, let's say you a planning a rafting trip. (This scenario is not the one modeled in the picture.) The small rafts are cheaper but only hold up to 4 people. The larger raft costs a little more but can hold up to 8. How many people can you take before it becomes cheaper to take big rafts? You can graph the two equations on the same graph. The point at which the two lines cross is where the bigger boats become less expensive.