Question

1. the graph shows how many bottles a machine fills in a certain number of seconds. part a what is the constant of proportionality, and what does it mean in this situation?

Explanation:

Step1: Recall the formula for constant of proportionality

For a proportional relationship $y = kx$, the constant of proportionality $k=\frac{y}{x}$. We can pick a point on the graph. Let's take the point $(15, 400)$.

Step2: Calculate the constant of proportionality

$k=\frac{400}{15}=\frac{80}{3}\approx26.67$.

Step3: Interpret the constant of proportionality

The constant of proportionality $\frac{80}{3}$ means that the machine fills $\frac{80}{3}$ (or approximately 26.67) bottles per second.

Answer:

The constant of proportionality is $\frac{80}{3}$, and it means the machine fills $\frac{80}{3}$ bottles per second.