The Rectangle Area Mystery
Watch how length and width dance to keep area constant.
Equation
y = 10 / x
Graph
Table
| x | y |
|---|---|
| 1 | 10 |
| 2 | 5 |
| 3 | 3.33 |
| 4 | 2.5 |
| 5 | 2 |
| 6 | 1.67 |
| 7 | 1.43 |
| 8 | 1.25 |
| 9 | 1.11 |
| 10 | 1 |
What this lesson covers
What you do
You shape the function y = k / x and watch the graph answer.
Challenges to clear
- Find the constant k if length = 4 and width = 5.
- Check: does the curve pass through (4, 5)?
- The rectangle is three deep now: width = area ÷ (3 × length). Slide m to 3.
- Now the area: at length 5 the width must be 4. Multiply the two and the product is fixed — that is what inverse variation means.
Check yourself
In inverse variation, if x doubles, what happens to y?
Which equation represents an inverse variation?
- y is halved — correct
- y doubles
- y stays the same
- y becomes four times larger
- y = 5 / x — correct
- y = 5 * x
- y = x - 5
- y = x + 5
Think about it
- If we double the constant area k, what happens to the width y when length x is 2?