Chapter 2: Linear Relationships Notes

Graphing straight lines from tables and rules, gradient as a rate of change, the equation y = mx + c, direct variation and building linear models of real costs.

Sections

  1. 2A Graphing linear relationships Mastered

    Making a table of values from a rule, plotting real data with sensible axes, recognising a linear relationship, and reading values from the graph by interpolation and extrapolation.

  2. 2B Gradient and intercept in context Mastered

    Finding the gradient of a line as rise over run, reading it as a rate with units, and interpreting the vertical intercept as the starting value or fixed cost.

  3. 2C Writing the rule y = mx + c Mastered

    Writing a linear rule in the form y = mx + c from a description, from a graph, or from two data points, using letters that suit the context.

  4. 2D Direct variation Mastered

    Relationships of the form y = kx, finding the constant of variation from one pair of values, conversion graphs such as currency, and telling direct variation apart from other linear models.

  5. 2E Linear models and their limits Mastered

    Using linear models to compare plans and find break-even points, cost and revenue for a small business, and recognising when a straight-line model stops making sense.

Formula sheet