Mid-Chapter Quiz
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Check whether the product of the two variables remains constant.
Yes, see solution.
We want to determine whether the relationship between the variables in the given table is an inverse variation.
| x | y |
|---|---|
| 2 | 8 |
| 4 | 4 |
| 8 | 2 |
| 16 | 1 |
Inverse variations can be expressed in three ways as an equation.
x y= k, y=k/x, or x=k/y
In the above formulas, k is the constant of variation and k cannot be 0. Let's test to see if the product of x and y is constant for the given values.
| x | y | xy |
|---|---|---|
| 2 | 8 | 2* 8= 16 |
| 4 | 4 | 4 * 4= 16 |
| 8 | 2 | 8* 2= 16 |
| 16 | 1 | 16* 1= 16 |
The product of each pair is 16. This means that xy=16, and y varies inversely with x.