Question

circle a with radius ab is shown. suppose x represents the radius and y represents the circumference. choose the statement that best describes the constant of proportionality, $\frac{y}{x}$, for the relationship between radius and circumference. there is no constant of proportionality because it is not a proportional relationship. the constant of proportionality is $pi$. the constant of proportionality is $2pi$. the constant of proportionality is $2pi^{2}$.

Explanation:

Step1: Recall circle - circumference formula

The formula for the circumference of a circle is $y = 2\pi x$, where $y$ is the circumference and $x$ is the radius.

Step2: Find the constant of proportionality

For a proportional relationship $y=kx$ (where $k$ is the constant of proportionality), comparing $y = 2\pi x$ with $y=kx$, we get $k = 2\pi$. Since $\frac{y}{x}=\frac{2\pi x}{x}=2\pi$ (for $x
eq0$).

Answer:

The constant of proportionality is $2\pi$