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? And EXPLAIN how you know.

A) The equation is y = 50x + 200, and the relationship is proportional because it forms a linear equation.
B) The equation is y = 200 - 50x, and the relationship is proportional because it forms a linear equation.
C) The equation is y = 200/x + 50, and the relationship is proportional because it forms a hyperbolic function.
D) The equation is y = 200x + 50, and the relationship is not proportional because it forms a quadratic equation.

Answer 1

The correct equation is y = 50x + 200, and the relationship is proportional because it forms a linear equation.

Step-by-step explanation:

The correct equation to show the total cost of Hannah's cell phone plan is y = 50x + 200. The relationship between the time she has the plan and the total cost is proportional because it forms a linear equation.

Let's break it down:

1. The start-up fee of $200 is a one-time fixed cost, which is represented by the constant term 200 in the equation.
2. The charge of $50 per month is a variable cost that depends on the number of months, which is represented by the coefficient of x in the equation.
3. A linear equation represents a proportional relationship because it forms a straight line when graphed.