1. Inverse Variation
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What does plotting the points on a coordinate plane suggest?
Variation: Direct
Explanation: The data in the table can be represented by the equation y=2x.
We want to determine whether the relationship between the variables in the given table represents a direct variation or an inverse variation. Let's see what happens if we plot the points on a coordinate plane.
We can see that this might be a direct variation relationship. y=kx or k=y/x In the above formulas, k is the constant of variation and k cannot equal 0. Let's test to see if the quotient of y and x is constant for the given values.
| x | y | y/x |
|---|---|---|
| 1 | 2 | 2/1 = 2 |
| 4 | 8 | 8/4 = 2 |
| 8 | 16 | 16/8 = 2 |
| 12 | 24 | 24/12 = 2 |
The quotient of each pair is constant and it is equal to 2. Therefore, it is a direct variation y=2x.