Which of the following sets of ordered pairs is not a direct variation? (0, 0); (-2, 4); (3, -6) (1, 1); (-2, -2); (3, 3) (10, 2); (15, 3); (20, 4) (0, 0); (1,
(-2,4) (3,-6)
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In order to determine if a set of ordered pairs represents a direct variation, we need to check if there is a constant ratio between the corresponding x and y values.
Let's analyze the given sets of ordered pairs:
1. (0, 0); (-2, 4); (3, -6)
To find the ratio, we divide the y-value by the x-value for each pair:
- For (0, 0), 0/0 is undefined.
- For (-2, 4), 4/-2 = -2.
- For (3, -6), -6/3 = -2.
Since the ratio is constant (-2) for all the pairs, this set of ordered pairs represents a direct variation.
2. (1, 1); (-2, -2); (3, 3)
Calculating the ratios:
- For (1, 1), 1/1 = 1.
- For (-2, -2), -2/-2 = 1.
- For (3, 3), 3/3 = 1.
The ratio is constant (1) for every pair, indicating that this set of ordered pairs represents a direct variation.
3. (10, 2); (15, 3); (20, 4)
Upon finding the ratios:
- For (10, 2), 2/10 = 0.2.
- For (15, 3), 3/15 = 0.2.
- For (20, 4), 4/20 = 0.2.
Again, the ratio is constant (0.2) for all the pairs, demonstrating a direct variation.
4. (0, 0); (1, ?
To check for direct variation, let's calculate the ratio for the pair (1, ?):
- For (1, ?), we can't determine the ratio since the x-value is 0.
Thus, we can conclude that the set of ordered pairs (0, 0); (1, ?) does not represent a direct variation since we cannot calculate the ratio due to a zero divisor.
In summary, the set of ordered pairs that is not a direct variation is (0, 0); (1, ?).