#NumberAndAlgebra #Core >[!info]- [Linear relationships | NSW Curriculum Website](https://curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-k-10-2022/content/stage-4/fa6ebf0c74) >- MA4-LIN-C-01 creates and displays number patterns and finds graphical solutions to problems involving linear relationships ## 📖 Prior Knowledge | Content | Prior knowledge | Used for | | ------------------------------ | -------------------------------------------------- | --------------------------------------------------------------------------------------------------------- | | [[Multiplicative Relations B]] | - geometric number patterns involving multiples | - analysing geometric spatial sequences as linear relationships | | [[Geometric Measure A]] | - first quadrant of number plane | - plotting and identifying points on a Cartesian plane | | [[Computation with Integers]] | - operations with integers | - applying the equation of a linear relationship | | [[Algebraic Techniques]] | - substitution<br>- generalising relationships<br> | - constructing a table of values from an equation<br>- establishing the equation of a linear relationship | | [[Equations]] | - solving two-step equations | - applying the equation of a linear relationships<br>- solving equations graphically | ## [[Plot and identify points on the Cartesian plane.pdf]] - Plot and label points on the Cartesian plane of given coordinates, including those with coordinates that are not whole numbers - Identify and record the coordinates of given points on the Cartesian plane, including those with coordinates that are not whole numbers ## [[Plot linear relationships on the Cartesian plane.pdf]] - Construct a geometric pattern and record the results in a table of values - Represent a given number pattern (including decreasing patterns) using a table of values - Describe a number pattern in words and generate an equation using algebraic symbols - Apply an equation generated from a pattern to calculate the corresponding value for a smaller or larger number - Recognise that a linear relationship can be represented by a number pattern, an equation (or a rule using algebraic symbols), a table of values, a set of pairs of coordinates and a line graphed on a Cartesian plane, and move flexibly between these representations - Explain that there are an infinite number of ordered pairs that satisfy a given linear relationship by extending a line joining a set of points on the Cartesian plane - Compare similarities and differences of multiple straight-line graphs on the same set of axes using graphing applications - Describe linear relationships in real-life contexts and solve related problems ## [[Solve linear equations using graphical techniques.pdf]] - Recognise that each point on the graph of a linear relationship satisfies the equation of a line - Apply graphs of linear relationships to solve a corresponding linear equation using graphing applications - Graph 2 intersecting lines on the same set of axes and identify the point of intersection using either graphing applications or a table of values - Verify that the point of intersection satisfies the equations of both lines