Question 5: Proportional and Non-Proportional Relationships
Chose an equation from the list that represents a proportional relationship and
another that represents a non-proportional relationship and write them here.
Proportional __________________________
Non-Proportional __________________________
Graph them together on the following coordinate grid.
What do you notice about the similarities of the two graphs? What do you notice
about the difference between the two graphs?
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
Proportional: y = 2x
Non-Proportional: y = x^2
Graph on a coordinate grid:
Proportional (y = 2x): a straight line that passes through the origin (0,0) with a slope of 2.
Non-Proportional (y = x^2): a curved line that does not pass through the origin.
Similarities: Both graphs are continuous and have a range of values for both x and y. They both increase in value as x increases.
Differences: The proportional graph is a straight line, while the non-proportional graph is a curved line. The non-proportional graph does not pass through the origin, while the proportional graph does.
To be proportional graphically means that the relationship between the x and y values can be represented by a straight line passing through the origin. To be non-proportional means that the relationship between the x and y values cannot be represented by a straight line passing through the origin.
Real-world scenario for the proportional graph (y = 2x): The relationship between the number of hours worked and the amount of money earned, if someone earns $2 for every hour worked.
Overall, the key difference between proportional and non-proportional relationships lies in the shape of the graph and whether it passes through the origin.