To determine which of the provided tables represents a linear relationship and is also proportional, we need to check each set of points to see if they form a linear equation of the form \( y = mx + b \) and if they pass through the origin (meaning \( b = 0 \)).
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Table 1:
- \( x: 2, 3, 4 \)
- \( y: -3, 0, 3 \)
Here, the changes in \( y \) values are not consistent when you observe the ratio of \( \frac{y}{x} \). Specifically, at \( x = 3 \), \( y = 0 \). The point (0, -3) would need to exist for this to be proportional, but it leads to a linear equation with a \( b \neq 0\).
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Table 2:
- \( x: 4, 2, 0 \)
- \( y: -2, -1, 0 \)
Again, the points don't form a line that passes through the origin and their ratios are inconsistent, such as at \( x = 4\) leading to different values of \( y \).
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Table 3:
- \( x: -2, 1, 4 \)
- \( y: 0, 1, 2 \)
Here, with \( y = 1 \) when \( x = 1 \) and point (0, 0) doesn't exist, we see this does not confirm proportionality through the origin.
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Table 4:
- \( x: 0, 1, 2 \)
- \( y: -4, 0, 4 \)
Here, observe:
- \( (0, -4), (1,0), (2,4) \)
The ratio of \( \frac{y}{x} \) is not consistent which leaves it non-proportional.
Let’s summarize:
- None of the tables exhibit a proportional relationship because they do not all go through the origin, and thus they do not have a constant ratio of \( y/x \) throughout their entries.
Conclusion: None of the provided tables represents a linear relationship that is also proportional.