Graphing Linear Equations — NSW Year 8 Maths
Plotting points, finding rules from patterns and tables, and drawing straight-line graphs to solve equations. Eight subtopics and 160 practice questions, each with a fully worked solution, aligned to NESA outcome MA4-LIN-C-01.
Graphing Linear Equations in NSW Year 8
A linear relationship changes by the same amount at every step, so its points line up on a straight line when they are graphed. In Year 8, students move between four ways of showing one: a number pattern, a rule such as \(y = 2x + 3\), a table of values and a graph on the number plane. They then use the graphs to solve equations and to find where two lines cross.
The eight subtopics below start with the number plane, move through finding rules for patterns and tables, then graph lines, find the rule for a given line, solve equations graphically and finish with intersecting lines. Graphing Linear Equations is one of the 14 topics in NSW Year 8 Maths and sits in the Number and Algebra strand (NESA outcome MA4‑LIN‑C‑01). Everything here is done without gradient formulas; in Stage 5 the same ideas lead to gradient, the form \(y = mx + c\) and solving pairs of equations algebraically.
Subtopics
Graphing Linear Equations: common questions
What is a linear relationship?
It is a relationship in which \(y\) changes by the same amount every time \(x\) goes up by 1. Its table of values has a constant step and its points lie on a straight line, as for \(y = 3x - 1\).
How do you find the rule from a table of values?
Find how much \(y\) changes when \(x\) goes up by 1; that number multiplies \(x\). Then add the value of \(y\) when \(x = 0\). If \(y\) is 5, 8, 11 and 14 for \(x = 0, 1, 2, 3\), the rule is \(y = 3x + 5\).
How do you solve an equation using a graph?
Graph the rule on the left side, draw the horizontal line for the number on the right side, and read the \(x\)-value where they cross. To solve \(2x - 1 = 5\), draw \(y = 2x - 1\) and \(y = 5\); they meet where \(x = 3\).
Which NESA outcome covers graphing linear equations?
Linear relationships sit in Stage 4 of the NSW Mathematics K–10 Syllabus (2022) under outcome MA4‑LIN‑C‑01, which covers patterns, rules, tables of values, straight-line graphs and solving equations with graphs. It is usually taught in Year 8.
What comes after graphing linear equations?
In Stage 5, students meet gradient and equations written as \(y = mx + c\), work out the midpoint and the length of an interval, and solve pairs of equations algebraically as well as with graphs. Reading graphs is also used straight away for travel graphs in Time and Travel.