Question

a mysterious flying superhero known as blue sky protects the good citizens of rockport. unknown to these citizens, blue sky is actually mild - mannered pam, a scientist in a flying suit. before pam can fly in the suit, she needs to charge its battery. the graph shows the proportional relationship between the number of hours pam has charged her flying suit, x, and the number of hours she can fly, y. (graph: y - axis labeled flight hours from 1 to 10, x - axis labeled hours charged from 1 to 10, with a line passing through (8, 4))

Explanation:

Step1: Recall proportional relationship formula

For a proportional relationship, \( y = kx \), where \( k \) is the constant of proportionality.

Step2: Use the point \((8, 4)\) to find \( k \)

Substitute \( x = 8 \) and \( y = 4 \) into \( y = kx \): \( 4 = k \times 8 \).
Solve for \( k \): \( k=\frac{4}{8}=\frac{1}{2} \).

Step3: Determine the relationship

The equation of the line is \( y=\frac{1}{2}x \), meaning for every 2 hours charged, Pam can fly 1 hour (or the ratio of flight hours to charge hours is \( \frac{1}{2} \)).

Answer:

The constant of proportionality \( k \) is \( \frac{1}{2} \), and the relationship is \( y = \frac{1}{2}x \) (if the question was to find the proportionality or equation; adjust based on actual question, but since the graph is about proportional relationship, this is the key result from the graph analysis).