Question

the student council is decorating the gym for the school dance. they are hanging strands of twinkle lights. there is a proportional relationship between the number of strands they hang, x, and the number of twinkle lights, y. x (strands) y (twinkle lights) 1 25 2 50 3 75 4 100 what is the constant of proportionality? write your answer as a whole number or decimal. twinkle lights per strand

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 first - pair where $x = 1$ and $y = 25$.

Step3: Calculate the constant of proportionality

$k=\frac{y}{x}=\frac{25}{1}=25$. We can check with other pairs. For $x = 2$ and $y = 50$, $k=\frac{50}{2}=25$; for $x = 3$ and $y = 75$, $k=\frac{75}{3}=25$; for $x = 4$ and $y = 100$, $k=\frac{100}{4}=25$.

Answer:

25