Question

roxanne is measuring the diameter and the radius of different - sized circles. 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 proportional - relationship definition

Two variables $x$ and $y$ have a proportional relationship if $y = kx$, where $k$ is a non - zero constant (constant of proportionality), and the graph of the relationship is a straight line passing through the origin $(0,0)$. The given graph is a straight line and passes through the origin $(0,0)$ since when $x = 0$, $y=0$ (a circle with radius $0$ has diameter $0$). So, $x$ and $y$ have a proportional relationship.

Step2: Find the constant of proportionality

The formula for the diameter $y$ of a circle in terms of its radius $x$ is $y = 2x$. The constant of proportionality $k$ in the equation $y=kx$ is $2$. This means that for every 1 - inch increase in the radius of the circle, the diameter increases by 2 inches.

Answer:

yes
2