Question

part a
what is the constant of proportionality, and what does it mean in this situation?
use the drop - down menus to show and explain your answer.
the constant of proportionality is the machine caps bottles in

Explanation:

Step1: Calculate the constant of proportionality

The formula for the constant of proportionality \( k \) in a proportional relationship \( y = kx \) is \( k=\frac{y}{x} \).
Using the point \((15,300)\) (from the graph where \(x = 15\) seconds and \(y=300\) bottles), \(k=\frac{300}{15}=20\).

Step2: Interpret the constant of proportionality

The constant of proportionality \(k = 20\) means that for every unit increase in \(x\) (seconds), \(y\) (number of bottles) increases by \(k\).

Answer:

The constant of proportionality is \(20\), the machine caps \(20\) bottles in \(1\) second.