To determine if the given points represent a linear relationship, we can check if the slope between consecutive points remains constant. The points you provided are:
\[ (-2, -12), \ (-1, 10), \ (0, 8), \ (1, 6), \ (2, 4), \ (3, 2) \]
We will calculate the slopes between each pair of consecutive points:
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Between (-2, -12) and (-1, 10): \[ \text{slope} = \frac{10 - (-12)}{-1 - (-2)} = \frac{10 + 12}{-1 + 2} = \frac{22}{1} = 22 \]
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Between (-1, 10) and (0, 8): \[ \text{slope} = \frac{8 - 10}{0 - (-1)} = \frac{-2}{1} = -2 \]
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Between (0, 8) and (1, 6): \[ \text{slope} = \frac{6 - 8}{1 - 0} = \frac{-2}{1} = -2 \]
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Between (1, 6) and (2, 4): \[ \text{slope} = \frac{4 - 6}{2 - 1} = \frac{-2}{1} = -2 \]
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Between (2, 4) and (3, 2): \[ \text{slope} = \frac{2 - 4}{3 - 2} = \frac{-2}{1} = -2 \]
From our calculations, we can see that the slope is not constant between the first pair of points and the subsequent pairs:
- The slope between the first pair ((-2, -12) to (-1, 10)) is 22.
- All other slopes are -2.
Since the slopes differ, these points do not represent a linear relationship.