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Finding the equation of a straight line from its gradient and a point

Algebra · Grade 4–6

Strand: Algebra Substrand: Graphs and coordinates Sparx code: U477 Sparx levels: 2, 3, 4, 5

Key steps (method)

  • Simplify both sides first (remove brackets and collect like terms).
  • Get all the x terms on one side and constants on the other.
  • Use inverse operations step-by-step (undo +/− then ×/÷).
  • If there are fractions, clear them by multiplying through by the LCM of denominators.
  • Check by substituting your answer back into the original.

Common mistakes

  • Doing different operations to the two sides of the equation.
  • Sign errors when moving terms across the equals sign.
  • Dropping brackets or mis-handling negatives.
  • Not checking the final answer.

Quick notes

  • If you get stuck, try a simpler version of the problem first or plug in easy numbers to test your method.
  • For multi-step questions, label each step and keep intermediate results.
  • For exam questions, always aim to make your work “mark-scheme readable”.

Self-assessment

  • Can I define it? Write a one-sentence definition of Finding the equation of a straight line from its gradient and a point (or the key term in the question).
  • Can I do it? Do 3 questions: one easy, one standard, one harder. Don’t look at notes until you’ve tried.
  • Can I explain it? In 2–3 sentences, explain why the method works (or what would go wrong with a common mistake).
  • Can I check it? State one quick check (estimate, units, sign, reasonableness).

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Notes