The Magic Rectangle: Inverse Proportion
Watch how length and width change together while the area stays fixed.
Equation
y = 20 / x
Graph
Table
| x | y |
|---|---|
| 1 | 20 |
| 2 | 10 |
| 3 | 6.67 |
| 4 | 5 |
| 5 | 4 |
| 6 | 3.33 |
| 7 | 2.86 |
| 8 | 2.5 |
| 9 | 2.22 |
| 10 | 2 |
What this lesson covers
What you do
You shape the function y = k / x and watch the graph answer.
Challenges to clear
- Make the Area k equal 40: with Length x = 5 the Width y must be 8.
- Same area, longer rectangle: doubling the Length to 10 must HALVE the Width to 4.
- The sweets are shared among TWO children per row, not one. Slide m to 2.
- Now find the total: with 5 rows each child gets 6. More children always means fewer each — the product never changes.
Check yourself
In an inverse proportion, what happens to y if x is doubled?
Which equation represents an inverse proportion?
- y becomes half its original value. — correct
- y becomes double its original value.
- y stays the same.
- y becomes zero.
- y = k / x — correct
- y = k * x
- y = x - k
- y = x + k
Think about it
- If we double the Area (k), what happens to the Width (y) for the same Length (x)?