Two variable quantities vary directly if the ratio of one to the other remains constant.
Direct variation describes a relationship between two variables that change together in a constant way. When one variable increases, the other increases at a steady rate. When one decreases, the other decreases at the same steady rate.
In direct variation, the ratio between the two variables stays the same.
For example, if we earn $10 per hour, then the total money we earn varies directly with the number of hours worked.
- 1 hour → $10
- 2 hours → $20
- 3 hours → $30
We can represent this relationship as y = kx.
Where k is the constant of variation.
Direct variation shows up in:
- Pay per hour
- Distance traveled at a constant speed
- Scaling shapes proportionally
When Do Students Learn About Direct Variation?
Students begin learning about direct variation when they study proportional relationships and algebra.
Grades 7–8 – Introduction to Direct Variation
Students explore proportional relationships and learn to recognize and write equations like y = kx.
Grades 9+ – Applying Direct Variation in Algebra
Students analyze graphs, solve equations, and apply direct variation to real-world problems in algebra and science.
