Two quantities are directly proportional when they change by the same scale factor. The direct proportion formula is y = kx, where k is the constant of proportionality. Dividing y by x gives the same constant for every matching pair of values.
Enter three values and leave one blank to solve a proportion, or enter all four values to test whether two ratios are equal.
When y = 3x, doubling x also doubles y while the ratio y/x remains equal to three.
What Is Direct Proportion?
Direct proportion describes two quantities whose ratio remains constant.
When one quantity is multiplied by a scale factor, the other quantity is multiplied by the same factor.
This creates equivalent ratios that can be checked with the Proportion Calculator.
Direct Proportion Formula
The standard formula is y = kx.
The letter k represents the constant of proportionality.
It tells you how many units of y correspond to one unit of x.
How to Find the Constant of Proportionality
Divide y by x.
For x = 4 and y = 12, divide 12 by four.
The constant is k = 3.
Example: Find Y in a Direct Proportion
Suppose y is directly proportional to x and k equals five.
When x equals seven, substitute into y = 5x.
The result is y = 35.
Example: Find X in a Direct Proportion
Suppose y = 4x and y equals 28.
Rearrange the formula as x = y divided by four.
The result is x = 7.
Write Direct Proportion as Equal Ratios
Two matching value pairs can be written as x1/y1 = x2/y2 when corresponding positions are kept consistent.
For x = 2, y = 6 and x = 5, y = 15, the ratios 2/6 and 5/15 are equal.
Cross multiplication confirms that both products equal 30.
Direct Proportion Table
When k equals three, every y-value is three times its matching x-value.
| x | y | y ÷ x |
|---|---|---|
| 1 | 3 | 3 |
| 2 | 6 | 3 |
| 4 | 12 | 3 |
| 7 | 21 | 3 |
| 10 | 30 | 3 |
How to Recognise Direct Proportion
Calculate y divided by x for several corresponding value pairs.
A constant quotient indicates direct proportion.
The relationship should also pass through zero because y equals zero when x equals zero.
Direct Proportion Graph
A direct proportion produces a straight line through the origin.
The constant k determines the slope of that line.
A larger positive k creates a steeper upward line.
Direct Proportion in Unit Prices
A fixed price per item creates a direct relationship between quantity and total cost.
If one item costs three dollars, x items cost 3x dollars.
Doubling the quantity doubles the total price.
Direct Proportion in Distance Problems
At a constant speed, distance is directly proportional to time.
If a vehicle travels 60 kilometres each hour, the formula is distance = 60 × time.
Travelling for three hours produces 180 kilometres.
Direct Proportion in Recipes
Ingredient quantities are directly proportional to the number of servings when the recipe ratio is preserved.
Doubling the servings requires doubling every ingredient.
Using different scale factors for ingredients would change the recipe balance.
Direct Versus Inverse Proportion
In direct proportion, the ratio y/x remains constant.
In inverse proportion, the product xy remains constant.
Direct quantities increase or decrease together, while inverse quantities move in opposite directions.
The quotient y/x remains constant.
The product x × y remains constant.
Common Mistakes
Do not assume that every increasing relationship is directly proportional.
Check that the ratio y/x remains constant.
Keep corresponding quantities in the same positions when writing ratios.
A straight line that does not pass through the origin is not a direct proportion.
Conclusion
Use y = kx for direct proportional relationships.
Find k by dividing y by x and confirm that it remains constant.
Use the Proportion Calculator to solve equivalent-ratio forms of direct proportion problems.
FAQs
What is the direct proportion formula?
The formula is y = kx.
How do I find k?
Divide y by x.
What stays constant in direct proportion?
The ratio y/x remains constant.
What does a direct-proportion graph look like?
It is a straight line passing through the origin.
Does doubling x always double y?
Yes, when x and y are directly proportional.