To determine the rate and slope for the data provided in the table, we can observe the relationship between the number of photos $p$ and the cost $C$.

Step 1: Identify the Rate of Change (Slope)

The rate of change, or slope, between two points $(p_1, C_1)$ and $(p_2, C_2)$ can be calculated using the formula: $\text{slope} = \frac{C_2 - C_1}{p_2 - p_1}$

Step 2: Calculate the Slope Between Points

Using any two points from the table, we can find the slope:

• Using $(p_1, C_1) = (5, 2.50)$ and $(p_2, C_2) = (10, 5.00)$: $\text{slope} = \frac{5.00 - 2.50}{10 - 5} = \frac{2.50}{5} = 0.50$

This calculation gives a slope of 0.50, meaning the cost increases by $0.50 for each additional photo.

Conclusion

The rate of change, or slope, of this relationship is: $\text{slope} = 0.50$

This slope indicates that for every additional photo, the cost increases by $0.50.

Would you like further details or have any other questions?

Here are five related questions to explore further:

1. What would be the cost for 25 photos based on this rate?
2. How can we express the relationship between $p$ and $C$ as an equation?
3. Is the relationship between the number of photos and cost linear, and why?
4. How would the cost change if the rate increased to $0.75 per photo?
5. How many photos could you get for $15 based on this rate?

Tip: When determining the rate of change, ensure you consistently use corresponding points to maintain accuracy.