Definition: A proportional relationship is a relationship between two quantities in which the ratio of one to the other is always the same constant value.
What is a proportional relationship?
Two quantities are proportional when one is always a constant multiple of the other. Double one, and the other doubles too.
How can you recognize one?
Check the ratio y/x in a table. If it never changes, the relationship is proportional.
- 3 hours, 54 miles: 54 / 3 = 18
- 5 hours, 90 miles: 90 / 5 = 18
- 8 hours, 144 miles: 144 / 8 = 18
Every ratio is 18, so Mathbot’s scooter travels 18 miles per hour proportionally.
What does the graph look like?
A straight line that passes through the origin (0, 0). A line that crosses the y-axis elsewhere is not proportional.
What is the equation?
y = kx, where k is the constant ratio, here y = 18x.
What is a common mistake?
Assuming any straight line is proportional. The cost of a 12 dollar entry plus 3 dollars per ride is linear, but 0 rides still costs 12 dollars, so the ratios of cost to rides vary and the relationship is not proportional.
Where to learn it
- Spotting Proportional Relationships in Tables and Graphs – lesson
- Writing and Using y = kx Equations – lesson