Question

this graph shows the relationship between the radius of the circle in inches, x, and the diameter of the circle in inches, y. do x and y have a proportional relationship? yes no 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 formula for diameter

The formula for the diameter \(y\) of a circle in terms of the radius \(x\) is \(y = 2x\). This is in the form \(y=kx\) (where \(k\) is the constant of proportionality), which is the equation of a proportional relationship. A proportional relationship has a straight - line graph that passes through the origin \((0,0)\). Looking at the graph, it is a straight line and passes through \((0,0)\).

Step2: Find the constant of proportionality

From the formula \(y = 2x\), comparing with \(y=kx\) (the general form of a proportional relationship \(y = kx\), where \(k\) is the constant of proportionality), we can see that \(k = 2\).

Answer:

Yes, the constant of proportionality is \(2\)