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Question

A mysterious flying superhero known as Blue Sky protects the good citizens of Oxford. Unknown to these citizens, Blue Sky is actually mild-mannered Trudy, a scientist in a flying suit. Before Trudy can fly in the suit, she needs to charge its battery.
There is a proportional relationship between the number of hours Trudy has charged her flying suit, x, and the number of hours she can fly, y.
x (hours charged) y (flight hours)
1 1
4 4
7 7
8 8
What is the constant of proportionality? Write your answer as a whole number or decimal.
flight hours per hour charged

Answer 1

To find the constant of proportionality in a proportional relationship, we can use the formula:

\[ k = \frac{y}{x} \]

where \( k \) is the constant of proportionality, \( y \) is the flight hours, and \( x \) is the hours charged.

From the provided data, we can choose any pair of \( (x, y) \) values since they all exhibit a proportional relationship. Let's take the first pair:

When \( x = 1 \), \( y = 1 \):

\[ k = \frac{1}{1} = 1 \]

Now let's check another pair for verification. Using \( x = 4 \), \( y = 4 \):

\[ k = \frac{4}{4} = 1 \]

Using \( x = 7 \), \( y = 7 \):

\[ k = \frac{7}{7} = 1 \]

Using \( x = 8 \), \( y = 8 \):

\[ k = \frac{8}{8} = 1 \]

In all cases, the constant of proportionality \( k \) is 1.

Therefore, the constant of proportionality is 1 flight hour per hour charged.