Question

copy (1) circles, proportional relationship, scale drawing
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a pool is being filled with water at a constant rate. the table shows how much water is in the pool after the specified time.

time(minutes)	water volume (gallons)
100	1,200
150	1,800

identify the constant of proportionality.
gallons per minute

Explanation:

Step1: Recall proportion formula

The formula for a proportional relationship is $y = kx$, where $k$ is the constant of proportionality. Here, $y$ is water - volume and $x$ is time. So, $k=\frac{y}{x}$.

Step2: Select a data - pair

Let's take the first data - pair: $x = 50$ minutes and $y = 600$ gallons.

Step3: Calculate the constant of proportionality

$k=\frac{600}{50}=12$. We can double - check with other data pairs. For $x = 100$ and $y = 1200$, $k=\frac{1200}{100}=12$. For $x = 150$ and $y = 1800$, $k=\frac{1800}{150}=12$.

Answer:

12