A proportional relationship is any relationship between things that changes together. In other words, the objects being compared would have a relationship with each other in the way that they change. These relationships can be useful in many different situations.
Two types of proportional relationships are direct and inverse. In a direct relationship, as one object gets larger, the other object gets larger as well. An example of a direct proportional relationship would be buying an item at the grocery store. If one can of green beans costs $1, but you want to buy two cans, then you are seeing a direct proportional relationship in action. You know that the total cost of the two cans will be $2. The two items being compared in this example are the number of cans and the total cost. As the number of cans being purchased goes up, so does the total cost.
The opposite of a directly proportional relationship would be an inverse proportion. This type of relationship means that as one item gets larger, the other gets smaller. They are still related proportionally because their movements are still impacted by each other. However, they move in opposite ways. An example of this would be the relationship between the painting of a house and the number of people who are painting. If only one person is painting, it might take them 20 hours to paint the house, but if more people join, the total time for painting will decrease. If five people paint, the total time would be much smaller: four hours. As the number of people painting increases, the total time for painting the house decreases.