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: x - axis labeled hours charged from 0 to 10, y - axis labeled flight hours from 0 to 10, with a line passing through the origin and the point (8, 4))

Explanation:

Step1: Recall proportional relationship formula

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

Step2: Calculate slope \( k \)

Using the point \((8, 4)\), \( k=\frac{y}{x}=\frac{4}{8}=\frac{1}{2} \). So the equation is \( y = \frac{1}{2}x \). (If the question was to find the equation or slope, this is the process. Assuming we need the slope or equation, but since the problem isn't fully stated, but the graph is proportional, the key is identifying the relationship.)

Answer:

The constant of proportionality (slope) is \(\frac{1}{2}\), and the equation is \( y = \frac{1}{2}x \) (depending on the specific question, but based on the graph, this is the proportional relationship).