To determine the constant rate of change in this graph, we need to calculate the slope of the line, which represents how much the sale price (y) changes in relation to the retail price (x).

Step-by-Step Solution

1. Identify Points on the Line: The graph shows two clear points:

   • Point 1: $(20, 10)$
   • Point 2: $(40, 20)$

2. Calculate the Slope: The formula for slope (rate of change) is: $\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the points $(x_1, y_1) = (20, 10)$ and $(x_2, y_2) = (40, 20)$: $\text{slope} = \frac{20 - 10}{40 - 20} = \frac{10}{20} = 0.5$

3. Interpret the Rate of Change: The slope of 0.5 means that for each $1 increase in retail price, the sale price increases by $0.5. This suggests a proportional relationship between the retail price and the sale price, with the sale price being consistently 50% of the retail price.

Summary

• Constant Rate of Change (slope): 0.5
• Interpretation: The sale price is half of the retail price at any point on the graph.

Would you like more details on any part of this solution, or do you have additional questions?

Here are 5 related questions for further practice:

1. What would the sale price be if the retail price is $80, based on this rate of change?
2. How would the graph look if the rate of change were 1 instead of 0.5?
3. Can the constant rate of change be negative? What would that mean in this context?
4. What are the implications of a rate of change of 0 on a graph?
5. How would we interpret a rate of change greater than 1?

Tip: When identifying the rate of change from a graph, always confirm points clearly intersecting grid lines for accurate calculation.