Topic 1: Modelling with Linear Relationships

4 dot points, in syllabus order. Each dot point has a focused answer, with exam-style questions and worked answers where available.

How do we use a straight-line equation to model and predict from a real situation?

Construct and interpret linear functions of the form y = mx + c to model practical situations, identifying the meaning of the gradient and intercept.

How to build a linear model y = mx + c from a worded situation, interpret the gradient as a rate and the intercept as a starting value, and use the model to predict, with worked SACE-style examples.

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How do we model a situation whose rate of change shifts at certain points?

Construct, graph and interpret piecewise-linear models in which the rule changes over different intervals of the domain.

How to build a piecewise-linear model where different straight-line rules apply over different intervals, graph it, read its breakpoints, and use it to solve practical step-rate problems.

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How do we find the best decision when several linear constraints limit our choices?

Formulate linear programming problems with constraints and an objective function, identify the feasible region, and find the optimal solution at a vertex.

How to set up constraints and an objective function, graph and shade the feasible region, and use the corner-point principle to maximise or minimise the objective.

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How do we find the point where two linear models meet, and what does break-even mean?

Solve pairs of simultaneous linear equations algebraically and graphically, and interpret the solution as a break-even point in cost and revenue models.

How to solve two linear equations by substitution or elimination, find the break-even point where cost equals revenue, and interpret profit and loss regions.

8 min read →