Explain what is means graphically to be proportional. Explain what is means graphically to be non-proportional. Explain the difference between proportional and non-proportional.
Using your proportional graph, create a real-world scenario that would describe the graph.
When two variables are proportional, their relationship can be represented by a straight line that passes through the origin (0,0) on a graph. This means that as one variable increases, the other variable increases by a constant factor. The graph will have a constant slope and will never intersect the x or y-axis.
On the other hand, when two variables are non-proportional, their relationship cannot be represented by a straight line. The graph will have a curved shape or may even be discontinuous. In this case, the variables may increase or decrease independently of each other, or their relationship may change at different points.
The main difference between proportional and non-proportional relationships is the constant factor in proportional relationships. In a proportional relationship, the ratio between the two variables remains constant, while in a non-proportional relationship, this ratio can change.
For example, let's consider a proportional graph where the x-axis represents the number of hours worked and the y-axis represents the amount of money earned. As the number of hours worked increases, the amount of money earned also increases at a constant rate, represented by a straight line passing through the origin. This would be a proportional relationship.
In contrast, a non-proportional graph could represent the relationship between the amount of water added to a plant and the height of the plant. At first, adding more water might lead to a significant increase in plant height, but eventually, the plant may reach a point where adding more water does not result in further growth. The graph of this relationship would not be a straight line and would demonstrate a non-proportional relationship.
In few questions
Sure, here are a few questions to help you understand the concepts of proportional and non-proportional relationships:
1. Can you identify a proportional relationship from a graph by looking at its shape?
2. How does the slope of a graph change in a proportional versus a non-proportional relationship?
3. What does it mean for a graph to pass through the origin in a proportional relationship?
4. Give an example of a real-world scenario that would demonstrate a non-proportional relationship.
5. How would you determine if a relationship is proportional or non-proportional from a graph?