INVERSE VARIATION
Definition Of Inverse Variation
Inverse variation is a variation in which the variable y varies inversely as x, if there is a nonzero constant k such that xy = k or 
, where k ≠ 0.
More About Inverse Variation
In inverse variation, when one variable increases the other decreases in proportion so that the product remains the same always.
Video Examples: Inverse Variation
Example of Inverse Variation
The equations xy = 11, 
are examples of inverse variation.
Solved Example on Inverse Variation
Ques: Determine whether the following statement is true. If (r, a) and (v, f) both satisfy inverse variation, then 
.
Choices:
A. yes
B. no
Correct Answer: A
Solution:
Step 1: The formula for an inverse variation is xy = k, where k ≠ 0.
Step 2: Substitute (r, a) in the equation.
Step 3: ra = k
Step 4: Substitute (v, f) in the equation.
Step 5: vf = k
Step 6: So, ra = vf
Step 7: 
[Divide throughout by v.]
Step 8: [Divide throughout by a.]
Step 9: So, the given statement is true.
Quick Summary
- In inverse variation, as one variable increases, the other decreases proportionally.
- The product of the two variables remains constant.
🍎 Teacher Insights
Use real-world examples to illustrate inverse variation, such as the relationship between speed and time for a fixed distance.🎓 Prerequisites
- Algebra
- Variables
- Constants
Check Your Knowledge
Q1: If y varies inversely as x, and y = 4 when x = 3, what is y when x = 6?
Q2: Which equation represents inverse variation?
Frequently Asked Questions
Q: What happens to y when x doubles in an inverse variation?
A: y is halved.
Q: How do I find the constant of variation, k?
A: Multiply x and y (k = xy).