Solving Equations Graphically

Solving an equation graphically means using the graph of a rule to find the \(x\)-value that makes the equation true. To solve \(2x + 1 = 7\), draw \(y = 2x + 1\) and the horizontal line \(y = 7\), then read where they meet: \(x = 3\). In NSW Year 8 maths this links equations to linear graphs (NESA outcome MA4‑LIN‑C‑01).

You will read \(y\) from a given \(x\) and \(x\) from a given \(y\), test whether a point is on the line by substituting, and choose the horizontal line that solves an equation, including answers between grid lines such as \(x = 2.5\). You will check each answer by substitution and use graphs of a growing bean plant, melting snow and the profit from a school disco. It is part of Year 8 Graphing Linear Equations.