Question

edna is throwing a pool party to kick off the summer. her pool is empty, so she starts filling it with water from a garden hose. there is a proportional relationship between the time edna has been filling up the pool (in minutes), x, and the volume of water in the pool (in gallons), y. what is the constant of proportionality? write your answer as a whole number or decimal. x (minutes) 1 2 3 4 y (gallons) 23 46 69 92

Explanation:

Step1: Recall the formula for constant of proportionality

For a proportional relationship $y = kx$, the constant of proportionality $k=\frac{y}{x}$.

Step2: Choose a pair of values from the table

Let's take the pair $x = 1$ minute and $y=23$ gallons.

Step3: Calculate the constant of proportionality

$k=\frac{y}{x}=\frac{23}{1}=23$.
We can check with other pairs. For $x = 2$ and $y = 46$, $\frac{y}{x}=\frac{46}{2}=23$; for $x = 3$ and $y = 69$, $\frac{y}{x}=\frac{69}{3}=23$; for $x = 4$ and $y = 92$, $\frac{y}{x}=\frac{92}{4}=23$.

Answer:

23