Finding the Rule

Finding the rule means working out the equation that links \(x\) and \(y\) in a table, a set of points or a graph, such as \(y = 3x + 2\). In NSW Year 8 maths this is done from the change in \(y\) and the starting value, without gradient formulas (NESA outcome MA4‑LIN‑C‑01).

You will find the number that multiplies \(x\) from how much \(y\) changes each step, and the number added from the value when \(x = 0\), including decreasing tables, negative values and tables where \(x\) goes up in twos. You will fill in missing entries, check that a rule works for every column, decide between two suggested rules, read a rule from plotted points, and write rules for real costs such as bike hire. It is part of Year 8 Graphing Linear Equations.