Linear Modelling

Four real-world scenarios. In each one, three providers offer the same kind of service with different pricing. Your job is to model each provider's price as a linear function and compare them.

For every scenario you will

• Fill three tables — one per provider — with the cost (or savings) at each value of t from 0 up to 10. Each cell checks itself as you type.
• Write three algebraic rules — one per provider. The rule is in the form C = … t + … (or S = …). Type the whole rule yourself; the marker compares it to the correct one by evaluating both at several values of t, so equivalent forms (e.g. 15t + 30 and 30 + 15t) all count.
• Plot three lines on the shared grid. For each line you click two grid points that lie on that line. Pick whichever two values of t you like — they just have to land exactly on the line.

The four scenarios

• Scenario 1 · Gym memberships — sign-up fee + weekly cost
• Scenario 2 · Streaming services — sign-up fee + monthly cost
• Scenario 3 · Taxi rides — flagfall + per-km charge
• Scenario 4 · Savings plans — opening balance + weekly deposit

All Four Scenarios Modelled