To determine the constant of proportionality from the given points (6, 82.80) and (2, 27.60), we can use the formula for the constant of proportionality, which is calculated as:
\[ k = \frac{y}{x} \]
where \(y\) is the output value and \(x\) is the input value.
Let's calculate the constant of proportionality for both points:
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For the point (6, 82.80): \[ k_1 = \frac{82.80}{6} = 13.80 \]
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For the point (2, 27.60): \[ k_2 = \frac{27.60}{2} = 13.80 \]
Since both calculations provide the same constant of proportionality, we find that the constant of proportionality is:
\[ \boxed{13.80} \]