Phone Plan Comparison

Pre-Algebra · Axiom Academy

LESSON Comparing Phone Plans with Lines A monthly bill is just a fixed fee plus a per-minute rate — a straight line. Where two plans' lines cross, the better deal switches. 1. A Plan's Cost Is a Straight Line A plan's monthly cost has two parts: a fixed fee you pay no matter what, and a per-minute rate times the minutes you use. Written out, that's a linear equation — graph it against minutes and you get a straight line that starts at the fixed fee and climbs at the rate . Plan A: start at 20 , add 0.10 for every minute 2. Two Lines Cross at the Break-Even Point Now graph both plans on the same axes. Plan A starts low ( 20 ) but climbs fast ( 0.10 /min); Plan B starts high ( 40 ) but climbs slowly ( 0.05 /min). Two lines with different slopes must cross exactly once — and that crossing is the break-even point , where both plans cost the same. To find it, set the two costs equal and solve for the minutes m : 3. The Cheaper Plan Flips at the Crossing The break-even point splits the graph into two zones. To the left (few minutes), Plan A's line sits lower, so it's cheaper. To the right (many minutes), Plan B's line sits lower, so it wins. Watch the marker sweep across — the cheaper plan switches exactly at 400 minutes. Plan A is cheaper. Its low fixed fee wins out when you don't use many minutes — the high rate hasn't added up yet. Plan B is cheaper. Its low per-minute rate wins out for heavy use, even though it starts with a higher fixed fee.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.