Based on the table provided, here's how we can analyze the relationship between the number of side dishes and the total cost to determine the correct graph:
### Step-by-Step Analysis:
1. Identify the Data Points:
- For 2 side dishes, the total cost is \[tex]$8.50.
- For 4 side dishes, the total cost is \$[/tex]11.50.
- For 5 side dishes, the total cost is \[tex]$13.00.
- For 8 side dishes, the total cost is \$[/tex]17.50.
2. Plot the Points:
- (2, 8.50)
- (4, 11.50)
- (5, 13.00)
- (8, 17.50)
3. Determine the Relationship:
- Calculate the differences in the total cost as the number of side dishes increases to identify any patterns.
- Note the increase in cost for each additional side dish:
- From 2 to 4 side dishes: [tex]\( \Delta y = 11.50 - 8.50 = 3.00 \)[/tex]
- From 4 to 5 side dishes: [tex]\( \Delta y = 13.00 - 11.50 = 1.50 \)[/tex]
- From 5 to 8 side dishes: [tex]\( \Delta y = 17.50 - 13.00 = 4.50 \)[/tex]
4. Analyze the Rate of Change:
- Between 2 and 4 side dishes: [tex]\( \frac{3.00}{2 - 0} = 1.50 \text{ per dish} \)[/tex]
- Between 4 and 5 side dishes: [tex]\( \frac{1.50}{1 - 0} = 1.50 \text{ per dish} \)[/tex]
- Between 5 and 8 side dishes: [tex]\( \frac{4.50}{3 - 0} = 1.50 \text{ per dish} \)[/tex]
5. Determine the Pattern of Total Cost Increase:
- The increase in cost suggests a consistent rate of charge per side dish beyond the initial costs.
6. Identify the Graph:
- The graph should show a linear relationship because the cost increases by a constant amount per additional side dish after 4 dishes.
- Hence, the plot of the points (2, 8.50), (4, 11.50), (5, 13.00), and (8, 17.50) should form a straight line.
- Look for a graph with these coordinates plotted to see which one matches the derived linear relationship.
### Conclusion:
The correct graph will accurately depict the points (2, 8.50), (4, 11.50), (5, 13.00), and (8, 17.50) and will show the linear trend we calculated. Given these analyses, the most accurate graph is the one where these points align on a straight line, reflecting a consistent rate of increase.
