Your family is choosing between two phone plans. Use two-variable relationships to model the total cost over time, compare the plans with equations, and recommend the better deal.
Your family is comparing two monthly phone plans — Plan A and Plan B. Both charge the same amount every month (no activation fees), making this a proportional relationship perfect for y = kx. Work through four phases: identify the variables, write equations, build a cost table, and compare the plans to give a recommendation. Use your real numbers throughout.
Before writing any equation, decide what changes and what depends on what. Set Plan A's monthly cost and write its equation.
The independent variable x = months. The dependent variable y = total cost in dollars. If the monthly charge is constant, that amount is k. The equation y = kx means: total cost = monthly rate × number of months. At month 0, you have paid $0 (y = k × 0 = 0).
A table lets you see the total cost at a glance for each month. Generate Plan A's cost table for months 1 through 6 using your rate from Phase 1.
If k = 25: month 1 → 25 × 1 = $25; month 2 → 25 × 2 = $50; month 3 → 25 × 3 = $75, and so on. Each row increases by $25 because k = 25.
Enter Plan B's monthly rate and choose a number of months to compare. The calculator will show the total cost for each plan and tell you which is cheaper — and by how much.
Calculate each plan's cost at x months: Plan A total = kA × x, Plan B total = kB × x. Subtract to find the difference. The lower total is the cheaper plan at that point in time.
Think about the long-term picture. Use the equations to find the total cost at 12 months and decide which plan your family should choose.
Write a 3–5 sentence recommendation memo to your family. Use your equations, table values, and comparison numbers to support your choice.
| Category | 4 — Expert | 3 — Proficient | 2 — Developing |
|---|---|---|---|
| Identifying Variables | Independent and dependent variables named correctly with real-world justification | Both variables correctly identified | One variable correct or labels swapped |
| Writing the Equation | Equation y = kx written correctly; k identified as monthly rate in context | Equation is correct | Equation has minor error or k not explained |
| Table & Comparison | All cost table values correct; both plans compared accurately at chosen month | Table correct; comparison is accurate | Table partially correct or comparison attempted |
| Communication | Recommendation clearly justified with equations and specific dollar amounts | Recommendation uses most numbers | Recommendation unclear or missing key data |