Question

1. a. constant:

b. equation:
c. what does the constant mean for this situation?
walking speed

Explanation:

Step1: Find the constant of proportionality

The formula for a proportional relationship is \(y = kx\), where \(k\) is the constant. From the graph, when \(x = 2\) (hours), \(y = 1\) (mile). Using \(k=\frac{y}{x}\), we have \(k=\frac{1}{2}\).

Step2: Write the equation

Substituting \(k = \frac{1}{2}\) into \(y=kx\), the equation is \(y=\frac{1}{2}x\).

Step3: Interpret the constant

The constant \(k=\frac{1}{2}\) represents the speed. Since \(k = \frac{y}{x}\) (miles per hour), it means the walking speed is \(\frac{1}{2}\) mile per hour.

Answer:

a. \(\frac{1}{2}\)
b. \(y=\frac{1}{2}x\)
c. The constant \(\frac{1}{2}\) means the walking speed is \(\frac{1}{2}\) mile per hour.