Let’s determine the rate of change for each graph and interpret its meaning:

16. Points Scored for 3-Point Baskets

• The rate of change is the change in points scored divided by the change in the number of baskets.
• Observing the graph:
  • For every 1 basket, the points scored increase by 3 points.
• Rate of change: $\frac{\Delta y}{\Delta x} = \frac{3 \text{ points}}{1 \text{ basket}} = 3$.
• Meaning: Each 3-point basket scores 3 points.

17. Distance Sound Travels in Air

• The rate of change is the change in distance divided by the change in time.
• Observing the graph:
  • For every 10 seconds, the distance increases by 1 mile.
• Rate of change: $\frac{\Delta y}{\Delta x} = \frac{1 \text{ mile}}{10 \text{ seconds}} = 0.1 \text{ miles/second}$.
• Meaning: Sound travels at a constant speed of 0.1 miles per second in this situation.

18. Speed

• The rate of change is the change in speed divided by the change in time.
• Observing the graph:
  • Speed decreases by 16 ft/s for every 1 second.
• Rate of change: $\frac{\Delta y}{\Delta x} = \frac{-16 \text{ ft/s}}{1 \text{ second}} = -16 \text{ ft/s per second}$.
• Meaning: The speed is decreasing at a constant rate of 16 ft/s every second.

Summary of Rates of Change:

1. Graph 16: $3$ points per basket.
2. Graph 17: $0.1$ miles per second.
3. Graph 18: $-16$ ft/s per second.

Would you like a detailed explanation of any of these interpretations?

Related Questions:

1. What is the general formula for calculating the rate of change in a graph?
2. How can negative rates of change be interpreted in real-world scenarios?
3. Why is it important to use units when describing the rate of change?
4. Can a rate of change ever be zero? What does that signify?
5. How would the rate of change be affected if the graph's slope becomes steeper?

Tip:

Always ensure to identify the units for the variables on the graph's axes to provide context for the rate of change!