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Mathematics / Year 8 / Algebra
Curriculum content descriptions
graph linear relations on the Cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution (AC9M8A02)
Elaborations
- recognising that in a table of values, if the first difference between consecutive values of the dependent variable is constant, then it is a linear relation
- graphing linear functions and relations of the form \(x\;=\;a,\;y\;=\;a,\;x\;\leq\;a,\;x\;>\;a,\;y\leq\;a,\;y>\;a\) on the Cartesian plane for known values of \(a\)
- completing a table of values, plotting the resulting points on the Cartesian plane and determining whether the relationship is linear
- graphing the linear relationship \(ax+b\;=\;c\) for given values of \(a\), \(b\) and \(c\) and identifying from the graph where \(ax+b\;<\;c\) or where \(ax+b\;>\;c\)
- solving linear equations of the form \(ax+b\;=\;c\) and one-variable inequalities of the form \(ax+b\;<\;c\) or \(ax+b\;>\;c\) where \(a>0\) using inverse operations and digital tools, and checking solutions by substitution
- solving linear equations such as \(3x+7\;=\;6x-9\), representing these graphically, and verifying solutions by substitution
General capabilities
ScOT terms
Cartesian coordinates, Cartesian planes, Linear equations, Inequations