Question

roxanne is measuring the diameter and the radius of different - sized circles. there is a proportional relationship between the radius of the circle in inches, x, and the diameter of the circle in inches, y. x (radius in inches) y (diameter in inches) 10 20 13 26 14 28 20 40 what is the constant of proportionality? write your answer as a whole number or decimal. inches in diameter per inch in radius

Explanation:

Step1: Recall the proportionality formula

$y = kx$, where $k$ is the constant of proportionality.

Step2: Take a pair of values

Let's take $x = 10$ and $y = 20$.

Step3: Calculate the constant of proportionality

$k=\frac{y}{x}=\frac{20}{10}=2$. We can check with other pairs. For $x = 13,y = 26$, $k=\frac{26}{13}=2$; for $x = 14,y = 28$, $k=\frac{28}{14}=2$; for $x = 20,y = 40$, $k=\frac{40}{20}=2$. So the constant of proportionality is 2.

Answer:

2