Question

Hannah's cell phone plan has a start-up fee of $200, and there is a charge of $50 per month. Write an equation to show the total cost of her cell phone plan, where x is the number of months, and y is the total cost. Is the relationship between the time she has the plan and the total cost proportional?

Answer 1

The equation representing the total cost of Hannah's cell phone plan is y = 200 + 50x, where y is the total cost and x is the number of months. The relationship is not proportional due to the initial start-up fee.

Step-by-step explanation:

To write an equation that shows the total cost of Hannah's cell phone plan based on the number of months she has the plan, let's use x to represent the number of months and y to represent the total cost. Since there is a start-up fee of $200 (which is a fixed cost) and a recurring charge of $50 per month, the total cost can be calculated using the formula:y = 200 + 50x

In this equation, the intercept would be the start-up fee ($200) and the slope would be the cost per month ($50). To determine if the relationship is proportional, we have to consider whether the graph of the equation would pass through the origin (0,0). Since there is a start-up fee, the line would not start at the origin, meaning the total costs do not increase at a constant rate that includes zero. Therefore, this relationship is not proportional.