To find the constant of proportionality between the points on the graph, we need to determine how each point relates to the others in a proportional manner.
Given the points are at \(14\), \(21\), and \(28\), let's first calculate the ratios between the consecutive points:
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For the points 14 and 21: \[ k_1 = \frac{21}{14} = \frac{3}{2} = 1.5 \]
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For the points 21 and 28: \[ k_2 = \frac{28}{21} = \frac{4}{3} \approx 1.333 \]
Now, we can summarize the constant of proportionality:
- The ratio of \(21\) to \(14\) gives us \(1.5\).
- The ratio of \(28\) to \(21\) gives us approximately \(1.333\).
To determine a single constant of proportionality, we can refer to a specific interval, or if these points are meant to be part of a linear relationship, we note that the proportional intervals don't stay constant.
If we were to graph these points and fit a line through them, we'd see that the graph is not consistent across all intervals, which indicates it's not strictly linear with a single constant of proportionality.
If you're looking for a general approach for proportional relationships, then from the first interval, we see \(1.5\) from \(14\) to \(21\) can be referenced as a proportional change.
In summary, the constant of proportionality appears to vary between the points, with \(1.5\) being the ratio between the first two points, and \(1.333\) being the ratio between the last two points. If you're looking for a single consistent ratio, it would depend on how you define the proportional relationship and whether you consider averaging or taking the first segment.