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Interactive Lesson · Linear Functions

Which Phone Plan Actually Costs Less?

Drag the slider and let the crossing point give you the answer

Plan A: $20/mo + $0.25/min Plan B: $50/mo + $0.1/min
Step 1 · The question
At how many monthly minutes do plans A and B cost the same?
Move the vertical line and watch the two dots — when do they meet?
Minutes 240 min

How to read this chart

The horizontal axis is monthly minutes; the vertical axis is that month's total cost. The orange line is Plan A: cheap monthly fee, expensive per-minute rate. The blue line is Plan B: pricey monthly fee, cheap minutes. The dashed vertical line is the usage you dragged to, and the two dots show what each plan would charge.

Where the lines cross is the break-even point: below it, A wins; above it, B wins. The pale orange and pale blue shading marks each plan's territory.

Where the break-even point comes from

Set the two costs equal: 20 + 0.25x = 50 + 0.1x. Rearranging gives 0.15x = 30, so x = 200 minutes, where both cost $70. That's no coincidence — any pair of "monthly fee + per-minute rate" works the same way. Change the numbers and the formula verifies itself instantly.

Another way to see it: B's extra $30 monthly fee has to be earned back at $0.15 saved per minute — 30 ÷ 0.15 = 200 minutes to break even.

Try it

  • Raise A's rate to 0.30: does the crossing point move left or right? Why?
  • Drop B's monthly fee to 30: where does the break-even land now?
  • Make both rates equal: do the lines still cross? (Think parallel lines.)

FAQ

Where do I find my monthly minutes?
Check your carrier's app for the monthly usage summary, and average the last two or three months for a steadier picture. Plans with off-peak or weekend rates don't fit this simple model, so keep those exclusions in mind.
What about data?
This page models the simplest case: monthly fee + per-minute price. You can fold a data difference into the monthly fee — if B charges $10 more for data, set B's fee 10 higher. The reasoning is identical.
Is anything uploaded?
No. Charting and math happen entirely in your browser. The page makes no network requests and needs no account.

Tool: Phone plan calculator. Chinese version: 手机套餐怎么选最划算