Question

No, there is not a proportional relationship between time and the cost of the cell phone plan. in a proportional relationship, the ratio between the two variables would remain constant. but, the cost of the cell phone plan includes a starting cost of $120, which does not change with time. only the monthly charge of $30 increases with each month. therefore, the relationship between time and cost is not proportional as the cost increases linearly over time due to the recurring monthly charge.

Answer 1

The question deals with the concept of proportional relationships versus non-proportional relationships in a financial context, such as a cell phone plan with fixed and variable costs and creating a budget line based on available money and the costs of goods.

Step-by-step explanation:

The question involves understanding the concept of a proportional relationship in financial contexts such as cell phone plans and budget lines. It highlights that there is not a proportional relationship if there is a starting cost that does not change with time.

A proportional relationship would require the ratio of the two variables to remain constant. In the case of a cell phone plan with a fixed starting cost and a monthly charge, the total cost to the consumer increases linearly over time with each additional charge, representing a non-proportional linear relationship.

Furthermore, when considering a budget with fixed amounts and unit costs for items, the budget line equation helps determine all possible combinations of goods one can afford. For example, with a budget of $10, a round trip cost of $2, and a phone call cost of $0.05 per minute, Jeremy can afford various combinations of round trips and phone minutes. This use of algebra in budgeting illustrates how financial decision-making can benefit from mathematical equations and reasoning.