- Mathematics General
- Year 11
Linear equations and their graphs
approx. 10 hrs
6 topics
33 concepts
Build mastery in modelling and analysing linear relationships in practical contexts.
approx. 10 hrs
6 topics
33 concepts
Build mastery in modelling and analysing linear relationships in practical contexts.
Linear equations and their graphs uses linear equations and straight-line graphs to model and analyse the relationship between two variables. The scope of this program includes piecewise-linear and step graphs as well as the graphical representation of simultaneous linear equations to explore breakeven analysis.
This learning program is made up of the following 6 topics, broken down into 33 concepts.
Use a CAS calculator to solve a literal equation
Solve equations with one algebraic fraction
Equations with pronumerals on both sides
Generate and solve linear equations from word problems and interpret the results
Solve three-step equations
Solve one-step equations
Solve two-step equations
Find the equation of a line from two points using a CAS calculator
Construct a linear graph and generate a table of values using a CAS calculator
Finding the x - intercept at y=0
Find the equation of a line given the gradient and the y-intercept
Find the gradient of a line between two points using formulae
Reading the x and y intercept from a graph
Sketch a linear relationship from a table of values on a cartesian plane
Determine the gradient and y-intercept using the gradient-intercept form of a linear relationship
Use the gradient and y-intercept to graph a linear equation
Find the gradient of a line between two points using rise over run
Finding the y - intercept at x=0
Interpret linear models
Construct a linear model
Establish meaning for the gradient and intercepts in a practical context
Use a CAS calculator to find the point of intersection of two linear graphs
Solve simultaneous equations using a CAS calculator
Generate and solve linear simultaneous equations from word problems and interpret results
Solve linear simultaneous equations by finding the point of intersection of their graphs
Solve linear simultaneous equations using elimination method where one or both of the equations need to be modified
Solve linear simultaneous equations using substitution method
Solve linear simultaneous equations using elimination method
Apply break-even analysis to linear models
Sketch a step graph
Sketch a piecewise linear graph
Analyse step graphs
Use a piecewise linear function to model and solve practical situations
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