Question

homework
the graph below shows the distance run by a swift - moving lion cub.
a speedy simba

1. **what is the constant of proportionality in the graph above? explain.
2. **what does the point (0,0) represent? explain its meaning.
3. **what is the value of k in the point (1,k)? explain its meaning.

Explanation:

Step1: Identify proportional relationship

The graph shows distance \(d\) (feet) vs. time \(t\) (minutes), a proportional relationship \(d = kt\), where \(k\) is the constant of proportionality.

Step2: Calculate k using graph points

Pick a clear point, e.g., \(t=10\) min, \(d=400\) ft.
\(k = \frac{d}{t} = \frac{400}{10} = 40\)

Step3: Interpret (0,0) point

The point \((0,0)\) means \(t=0\) minutes, \(d=0\) feet.

Step4: Find k in (1,k)

Use \(k=40\), so the point is \((1,40)\).

Answer:

1. The constant of proportionality is 40. This is calculated by dividing distance by time (e.g., 400 feet / 10 minutes = 40), representing the lion cub's speed in feet per minute.
2. The point (0,0) represents that at 0 minutes (the start), the lion cub has run 0 feet. It is the starting point of the cub's run.
3. The value of \(k\) is 40. This means that in 1 minute, the lion cub runs 40 feet, which is the cub's constant speed.