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
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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.
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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.
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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.
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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.
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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.
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