Direct Proportion Formula and Examples
Direct proportion means two amounts change together by the same factor, so if x doubles, y doubles too. The direct proportion formula is y = kx. First find the constant k by dividing y by x, such as k = 20 ÷ 4 = 5.
Video Lesson
Watch and learn the basics
🎬 Did this video explain it clearly?
Flashcards
Review key concepts visually
%20What%20Is%20Direct%20Proportion.webp)
%20Direct%20Proportion%20Formula%20Example%201.webp)
%20Direct%20Proportion%20Formula%20Example%202.webp)
%20Direct%20Proportion%20Formula%20Example%203.webp)
What Is Direct Proportion?
- Two quantities are in direct proportion if they increase or decrease together.
- If x doubles, then y also doubles.
Direct Proportion Formula
- We use the formula y = kx, where k ≠ 0.
- A constant means k stays the same, when x and y change.
Example: Direct Proportion to x²
- If y is directly proportional to x², we write y = kx².
- Find k first using given pairs, then substitute the x value to find the wanted y value.
Example: Direct Proportion to √x
- If y is directly proportional to √x, we write y = k√x.
- Find the constant k first, then use the formula to calculate the wanted y value.
Practice Questions
Test your understanding
Which formula shows is directly proportional to ?
Correct! 🎉 +10 pointsNot quite right
Direct proportion is always written as . This means when increases, increases by the same factor.
is directly proportional to , and when , . What is when ?
Correct! 🎉 +10 pointsNot quite right
First, find by dividing 18 by 6, which is 3. Then multiply 3 by 12 to get .
is directly proportional to , and when , . What is when ?
Correct! 🎉 +20 pointsNot quite right
First, find : . So the formula is . Finally, plug in : .
is directly proportional to , and when , . What is when ?
Correct! 🎉 +20 pointsNot quite right
Start with the formula . Find by dividing 15 by , which gives . Substitute : .
is directly proportional to , and when , . What is when ?
Correct! 🎉 +20 pointsNot quite right
Start with the formula . Find by dividing 32 by , which gives . Set : , so and .
is directly proportional to , and when , . What is when ?
Correct! 🎉 +30 pointsNot quite right
Start with the formula . Find by dividing 18 by , which gives . Set : , so and .
Want to see the full working?
Interactive Activity
Explore direct proportion by solving y = kx problems step-by-step
Loading interactive widget...
Students Also Ask
The questions students bump into most on this topic
The symbol ∝ shows that y is directly proportional to x, written as y ∝ x. It tells you the two quantities change together by the same factor. You can rewrite the same relationship as the equation y = kx, where k is a constant.
Substitute a known pair of values into the formula and solve for k. For y = kx, divide y by x. For example, when y = 20 and x = 4, the constant is k = 20 ÷ 4 = 5. The constant then stays the same for every pair.
Yes. Direct proportion also works when y is proportional to x² or √x. You write y = kx² or y = k√x, then find k by substituting a known pair. The method stays the same; only the form of x changes.
Finding k first lets you write the complete formula, such as y = 5x. Once you know k, the relationship between x and y is fixed. You can then substitute any value of x and find the matching y. Without k, the formula is incomplete.
Two quantities are directly proportional when they change together by the same factor. If one doubles, the other doubles; if one triples, the other triples. In symbols you write y ∝ x, which becomes the equation y = kx for a constant k.