AC9M8A02

See also: Learning Areas / Mathematics / Mathematics / Algebra / Year 8

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

Elaborations

• AC9M8A02_E1 - 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
• AC9M8A02_E2 - 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 \(a\)
• AC9M8A02_E3 - completing a table of values, plotting the resulting points on the Cartesian plane and determining whether the relationship is linear
• AC9M8A02_E4 - 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 \(ax+b\;>\;c\)
• AC9M8A02_E5 - 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
• AC9M8A02_E6 - solving linear equations such as \(3x+7\;=\;6x-9\), representing these graphically, and verifying solutions by substitution

Achievement Standard Components

• ASMAT806 - They graph linear relations and solve linear equations with rational solutions and one-variable inequalities, graphically and algebraically.
• ASMAT807 - Students use mathematical modelling to solve problems using linear relations, interpreting and reviewing the model in context.
• ASMAT808 - They make and test conjectures involving linear relations using digital tools.