The equation for the data presented in the table and graph is: Number of Hours x $125 per Hour = Total Cost. Which of the following describes how the table, the graph, and the equation are related?
A) The table, graph, and equation all represent the same relationship.
B) The table and graph represent one relationship and the equation represents another.
C) The table, the graph, and the equation each represent different relationships.
D) The table and the equation represent one relationship and the graph represents another.
A) The table, graph, and equation all represent the same relationship.
To determine which option describes how the table, graph, and equation are related, let's analyze each option:
A) The table, graph, and equation all represent the same relationship.
This option implies that the table, graph, and equation all represent the relationship between the number of hours and the total cost. In other words, any change in the number of hours would directly result in a corresponding change in the total cost. To verify this, we can look at the table and graph. If changing the number of hours in the table leads to a proportional change in the total cost on the graph, and this relationship can also be described by the equation, then option A is correct.
B) The table and graph represent one relationship and the equation represents another.
This option suggests that the table and graph represent one relationship, while the equation represents a different relationship. To determine if this is true, we need to compare the information from the table and graph to the equation. If they all represent the same relationship, then this option is incorrect.
C) The table, the graph, and the equation each represent different relationships.
According to this option, the table, graph, and equation represent separate and distinct relationships. To confirm this, we need to analyze each element and see if they demonstrate different relationships. If they do not, then this option is incorrect.
D) The table and the equation represent one relationship and the graph represents another.
This choice states that the table and equation describe one relationship, while the graph represents a different relationship. To determine if this is the case, we need to examine the information from the table, graph, and equation, and compare them. If they correspond to different relationships, then this option is the correct answer.
To answer the question, we need to assess the relationship between the information presented in the table and the graph, and how they relate to the equation. If any changes in the number of hours lead to proportional changes in total cost, and this relationship is accurately described by the equation, then option A is the correct answer. Otherwise, option D is the correct answer.