# VCE Further Mathematics Units 3 and 4 – Graphs and Relations

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## Description

6.1 Straight Lines
6.2 Simultaneous Equations
6.3 Graphs
6.4 Inequalities Outcome Key knowledge • intercepts and slope of a straight-line graph and their interpretation in practical situations • graphical and algebraic solutions of simultaneous linear equations in two unknowns • intercepts, slope, maximum/minimum points and average rate of change of non-linear graphs and their interpretation in practical situations • graphical representation of relations of the form $y = kx^n$ for $x \ge 0$, where n ∈ {–2, –1, 1, 2, 3} • properties of graphs used to model situations involving two independent variables • linear inequalities in one and two variables and their interpretation in practical situations • linear programming and its application • the terms constraint, feasible region and objective function in the context of linear programming • the sliding-line method and the corner-point principle for identifying the optimal solution of a linear programming problem.Key skills • construct and interpret straight-line graphs, line segment graphs and step graphs used to model practical situations • construct from a table of values and interpret non-linear graphs used to model practical situations • solve practical problems involving finding the point of intersection of two straight-line graphs • solve graphically practical problems involving finding the point of intersection of a linear graph with a non-linear graph • use relations of the form $y = kx^n$ for x ≥ 0, where n ∈ {–2, –1, 1, 2, 3} to model and analyse practical situations • interpret graphs used to model situations involving two independent variables • graph linear inequalities in one or two variables and interpret them when used in practical situations • formulate a linear programming problem with two decision variables and solve graphically • extend the linear programming method of solution to include only integer solutions where required.