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A restaurant at the food court in a mall is offering a lunch special. The table shows the relationship between the number of side dishes and the total cost of the special.

Restaurant
Number of Side Dishes Total Cost
2 $8.25
4 $11.25
5 $12.75
8 $17.25

Which of the following graphs shows the relationship given in the table?
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 7 and 25 hundredths through the point 3 comma 11 and 75 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 7 and 75 hundredths through the point 3 comma 12 and 25 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 25 hundredths through the point 3 comma 9 and 75 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 5 tenths through the point 5 comma 13

1 answer

To determine which graph best represents the data from the table regarding the number of side dishes and the total cost, let's first analyze the provided information.

The relationship between the number of side dishes and the total cost is as follows:

  • For 2 side dishes, the total cost is $8.25
  • For 4 side dishes, the total cost is $11.25
  • For 5 side dishes, the total cost is $12.75
  • For 8 side dishes, the total cost is $17.25

From the points provided in the table, we can observe the costs for some specific number of side dishes:

  • At 0 side dishes, we can estimate by linear interpolation that the cost is likely to be around $5 to $7.
  • The cost steadily increases, indicating a linear relationship.

Next, we should calculate the cost per side dish to identify the slope or the rate of increase:

  • The increase from 2 to 4 side dishes is $11.25 - $8.25 = $3 for 2 side dishes, giving an average cost of $1.50 per each of those side dishes.
  • The increase from 4 to 5 side dishes is $12.75 - $11.25 = $1.50 for 1 side dish, which also supports the earlier calculation.

Looking at the four provided graphs:

  1. The first option involves a line from (0, 7.25) through (3, 11.75).
  2. The second option involves a line from (0, 7.75) through (3, 12.25).
  3. The third option involves a line from (0, 5.25) through (3, 9.75).
  4. The fourth option involves a line from (0, 5.5) through (5, 13).

To find the correct graph, we want to see:

  • If the graph closely aligns with the costs represented at 2, 4, 5, and 8 side dishes—and if the cost approximately matches our expectations for 0 side dishes around $5 to $7.

Based on the estimated values:

  • The values from the graphs need to align with the calculated costs of the lunch special.
  • Considering the general pattern of costs increasing linearly, significance must go to how the costs are represented starting near $5.

After analyzing the options:

  • The fourth graph (from point (0, 5.5) through the point (5, 13)) seems to suggest a reasonable fit for linear increase and is in line with a baseline around $5.50, thus it predicts reasonable costs for the number of side dishes represented.

Therefore, the best graph showing the relationship given in the table is likely the fourth graph (from point (0, 5.5) through point (5, 13)).