This worksheet introduces graphing linear relations on the Cartesian plane, teaching students to solve linear equations and inequalities both graphically and algebraically. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- A relation is linear if the first difference between consecutive y-values in a table is constant.
- Solving an equation means finding the value that makes both sides equal — undo operations in reverse order.
- A one-variable inequality (like 2x + 3 < 11) is solved the same way as an equation, using inverse operations.
- Unlike Year 7, Year 8 equations can have rational (fraction) solutions, not just natural numbers.
- Always verify a solution by substituting it back into the original equation or inequality and checking it holds true.
What your child will practise:
- Checking whether a table of values represents a linear relation by testing if the first difference is constant.
- Solving a linear equation using inverse operations, including when the variable appears on both sides.
- Solving a one-variable inequality using the same inverse-operation steps as an equation.
- Verifying a solution to an equation or inequality by substitution.
- Formulating a real situation as a linear equation or inequality, then solve it.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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