The Universal Calculation Engine
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The Universal Calculation Engine

Linear Relationships

y = mx + b: m is the rate per unit of x; b is the value of y when x = 0.

Start this lessonConstant rate in y equals mx plus b

y = mx + b in words

m is the change in y for each 1-unit increase in x. b is the y-value at x = 0. A fixed fee plus a per-use charge (rent + per mile, membership + per class) often fits this form.

Example

Phone plan: $20 flat plus $0.10 per minute. Minutes are x, cost is y: y = 0.10x + 20. Ten minutes: $21. One hundred: $30.

See the line

Mistakes

  • Calling every graph a line without checking points.
  • Confusing flat fee (b) with rate (m).

Use the calculator

FAQ

When is it not linear?

If equal steps in x do not produce equal steps in y, the graph is not a single straight line over that interval—use the right model (curve, exponential, etc.) for that data.