Direct Variation Formula
Direct variation is a proportional relationship y = kx that always passes through the origin — when one quantity doubles, so does the other.
The Formula
When to use: Distance varies directly with time at constant speed: .
Quick Example
Notation
What This Formula Means
A proportional relationship that always passes through the origin — when one quantity doubles, so does the other.
Distance varies directly with time at constant speed: .
Formal View
Worked Examples
Example 1
easyAnswer
First step
Full solution
- 2 Find : .
- 3 Equation: .
- 4 Check: when , ✓
Example 2
mediumExample 3
mediumCommon Mistakes
- Calling any straight line direct variation - it must pass through the origin ().
- Confusing direct with inverse variation - direct multiplies together; inverse keeps the product constant.
- Forgetting to check is the same for all pairs - if drifts, it isn't direct variation.
Why This Formula Matters
It is the cleanest form of proportionality (distance at constant speed, pay per hour) and the bridge to slope and inverse variation; students who miss the through-the-origin requirement misclassify any fee-plus-rate line as direct variation. Recognizing it by "When is , and does doubling double ?" — rather than by familiar numbers — is what lets a student tell it apart from inverse variation and general linear relationship and constant of proportionality in a mixed problem set.
Frequently Asked Questions
What is the Direct Variation formula?
A proportional relationship that always passes through the origin — when one quantity doubles, so does the other.
How do you use the Direct Variation formula?
Distance varies directly with time at constant speed: .
What do the symbols mean in the Direct Variation formula?
' varies directly as ' or ' is directly proportional to '
Why is the Direct Variation formula important in Math?
It is the cleanest form of proportionality (distance at constant speed, pay per hour) and the bridge to slope and inverse variation; students who miss the through-the-origin requirement misclassify any fee-plus-rate line as direct variation. Recognizing it by "When is , and does doubling double ?" — rather than by familiar numbers — is what lets a student tell it apart from inverse variation and general linear relationship and constant of proportionality in a mixed problem set.
What do students get wrong about Direct Variation?
The procedure for direct variation is the easy part; the trap is calling any straight line direct variation. Asking "When is , and does doubling double ?" first is what keeps a correct-looking calculation from being attached to the wrong concept.
What should I learn before the Direct Variation formula?
Before studying the Direct Variation formula, you should understand: proportionality, linear relationship.