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To determine at what number of months the plan **without a phone** becomes cheaper than the plan **with a phone**, we need to find the point at which the two lines on the graph intersect. This intersection point represents the time at which the total costs for both plans are equal. After this point, the "without phone" plan will be cheaper.

### Analyzing the Graph
1. The intersection appears to be at approximately **16 months** based on the graph.
2. Therefore, for months beyond this point (e.g., 17 months and higher), the **without phone** plan becomes cheaper.

### Conclusion
- The correct answer is likely **B: 17 months and higher**, because at 16 months, both plans have the same cost, and after that, the "without phone" plan will cost less.

Would you like a deeper explanation or help with any additional details?

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Here are some follow-up questions for further exploration:

1. How would the cost comparison change if the initial cost of the "with phone" plan were lower?
2. What factors could cause one plan to become more cost-effective than another earlier?
3. How can you calculate the intersection point using algebra if equations of the lines are given?
4. What happens to the comparison if both plans had different monthly rates?
5. How can such graphs be used to predict future expenses accurately?

**Tip:** To determine where two lines intersect on a graph, look for the exact point where they cross or set their equations equal if they are given.

The following figure shows two cell phone plans, one that comes with a phone and one without a phone. For what number of months is the plan without a phone cheaper?

Learn how to compare two cell phone plans using a graph to determine when the plan without a phone becomes cheaper. This problem involves linear equations and graph interpretation, perfect for students in Grades 8-10.

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