You are launching a streaming channel. Use two-variable relationships to model your subscriber growth, build a data table, read a graph, and write an equation that tells the whole story.
Your streaming channel gains the same number of subscribers every week — a perfect proportional relationship. Work through four phases: identify your variables, write the equation y = kx, build a data table, read the graph for specific values, and compare two channels to decide which grows faster. Fill in every section, hit Calculate or Check, and finish the checklist and growth report at the end. Then print your report.
Every relationship has two variables. One you control (independent); the other depends on it (dependent). Set your channel's weekly growth rate and let the equation appear.
The independent variable x = weeks. The dependent variable y = total subscribers. If you gain the same amount every week, that constant rate is k. The equation is y = kx — multiply k times the number of weeks to get the total subscribers.
A table of values shows the relationship between x and y at specific inputs. Generate your table for weeks 0 through 5 using your growth rate from Phase 1.
Fill in the equation for each row. If k = 50: week 0 → 50×0 = 0; week 1 → 50×1 = 50; week 2 → 50×2 = 100, and so on. The y values increase by k each time — that is what makes it proportional.
Use your equation to answer targeted questions — find y when you know x, and work backwards to find x when you know y.
To find y: substitute x into y = kx and multiply. To find x: divide y by k (x = y ÷ k). On the graph, the line passes through the origin (0, 0) and goes up steeply if k is large.
Compare your channel against a rival channel. Enter both growth rates and a number of weeks, then see which channel wins — and by how much.
Write a 3–5 sentence growth report that uses your equation, table values, and graph readings. Explain which variable is independent, which is dependent, and what your equation predicts.
| Category | 4 — Expert | 3 — Proficient | 2 — Developing |
|---|---|---|---|
| Identifying Variables | Independent and dependent variables named correctly with clear reasoning | Both variables correctly identified | One variable correct or labels swapped |
| Writing the Equation | Equation y = kx written and k explained in context | Equation is correct | Equation has minor error or k not justified |
| Table & Graph | All table values correct; graph readings (y given x, x given y) both accurate | Table correct; at least one graph reading correct | Table partially correct or graph reading attempted |
| Communication | Growth report uses all numbers and clearly explains the relationship | Report uses most numbers | Report unclear or missing key numbers |