Question

A proportional relationship between the number of yards, x, and the number of feet, y, is given. The values are:

\begin{align*} 2 & : 6 \\ 18 & : 54 \\ 24 & : 72 \\ 26 & : 78 \end{align*}

What is the constant of proportionality? Write your answer as a whole number or decimal. Feet per yard.
a) 3
b) 4.5
c) 6
d) 9

Answer 1

The constant of proportionality between yards and feet is 3, reflecting the conversion rate of 1 yard equaling 3 feet.

Step-by-step explanation:

The question is asking to find the constant of proportionality from the given set of values representing the relationship between yards (x) and feet (y). To determine this, we observe the given pairs of values and note that they must reflect the known conversion: 1 yard equals 3 feet. When you compare each pair of x and y values, you'll find that they all conform to this relationship, confirming that the constant of proportionality is indeed the number of feet per yard.

For example, taking the pair 2 yards to 6 feet, we divide 6 feet by 2 yards to find that there are 3 feet in each yard. This demonstrates that the constant of proportionality is 3. Thus, we can answer this question with confidence by stating that option a) 3 represents the correct constant of proportionality, translating to 3 feet per yard.