Answer:
The constant of proportionality is k = [tex]\frac{2}{3}[/tex] ⇒ B
Step-by-step explanation:
The form of the equation of the proportionality is y = k x, where
∵ Marjorie made 4 wreaths in 6 hours
→ Let y the number of wreath and x is the time of making them
∵ y = k x
∵ y = 4 and x = 6
→ Substitute them in the equation
∴ 4 = k(6)
∴ 4 = 6k
→ Divide both sides by 6 to find k
∵ [tex]\frac{4}{6}[/tex] = [tex]\frac{6k}{6}[/tex]
∴ [tex]\frac{2}{3}[/tex] = k
Let us use the other information to be sure it will give us the same value of k
∵ She made 6 wreaths in 9 hours
∴ y = 6 and x = 9
→ Substitute them in the equation
∵ 6 = k(9)
∴ 6 = 9k
→ Divide both sides by 9 to find k
∵ [tex]\frac{6}{9}[/tex] = [tex]\frac{9k}{9}[/tex]
∴ [tex]\frac{2}{3}[/tex] = k
∴ The constant of proportionality is k = [tex]\frac{2}{3}[/tex]
