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Bot GPT 4-o mini To identify the constant of proportionality from the given points, we can look for a consistent ratio of \( y \) to \( x \) for the points plotted.
The points given are:
- \( (0, 0) \)
- \( (2, 14) \)
- \( (4, 28) \)
- \( (6, 42) \)
- \( (8, 56) \)
- \( (10, 70) \)
- \( (12, 84) \)
We can calculate the ratio \( \frac{y}{x} \) for the non-zero points:
1. For \( (2, 14) \):
\[
\frac{14}{2} = 7
\]
2. For \( (4, 28) \):
\[
\frac{28}{4} = 7
\]
3. For \( (6, 42) \):
\[
\frac{42}{6} = 7
\]
4. For \( (8, 56) \):
\[
\frac{56}{8} = 7
\]
5. For \( (10, 70) \):
\[
\frac{70}{10} = 7
\]
6. For \( (12, 84) \):
\[
\frac{84}{12} = 7
\]
All the ratios are consistent and equal to 7.
Therefore, the constant of proportionality for this graph is \( 7 \).