Question

1. here is a graph of the radius and circumference measurements of several circles. what is a constant of proportionality in this relationship?

Explanation:

Step1: Recall the formula for the constant of proportionality

For a proportional relationship \(y = kx\), the constant of proportionality \(k=\frac{y}{x}\). Here, \(y\) is the circumference and \(x\) is the radius.

Step2: Use the given point \((3,6\pi)\) to find \(k\)

Substitute \(x = 3\) and \(y=6\pi\) into \(k=\frac{y}{x}\). So \(k=\frac{6\pi}{3}=2\pi\).
We can check with another point \((2,4\pi)\): \(k = \frac{4\pi}{2}=2\pi\), and with \((0.5,\pi)\): \(k=\frac{\pi}{0.5}=2\pi\)

Answer:

\(2\pi\)