AlgebraStudy Notes

Worked Example 1: Linear Equation

Part of Graphical SolutionsGCSE Mathematics

This study notes covers Worked Example 1: Linear Equation within Graphical Solutions for GCSE Mathematics. Revise Graphical Solutions in Algebra for GCSE Mathematics with 9 exam-style questions and 6 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 4 of 9 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 4 of 9

Practice

9 questions

Recall

6 flashcards

Worked Example 1: Linear Equation

Solve graphically: 3x - 6 = 0

Step 1 Rearrange to standard form

3x - 6 = 0

3x = 6

y = 3x - 6 (set LHS equal to y)

Step 2 Identify line properties

Gradient (m) = 3

y-intercept = -6

Line passes through (0, -6) and (2, 0)

Step 3 Find x-intercept

Where line crosses x-axis: y = 0

0 = 3x - 6

6 = 3x

x = 2

Step 4 Check solution

3(2) - 6 = 6 - 6 = 0 ✓

Keep building this topic

Read this section alongside the surrounding pages in Graphical Solutions. That gives you the full topic sequence instead of a single isolated revision point.

Practice Questions for Graphical Solutions

A straight line y = 3x − 6 is plotted on a graph. Where does the solution to 3x − 6 = 0 appear on the graph?

  • A. Where the line crosses the y-axis
  • B. Where the line crosses the x-axis
  • C. At the origin
  • D. At the turning point of the line
1 markfoundation

A student tries to solve the simultaneous equations y = 3x + 2 and y = 3x − 5 graphically. Explain what they will see on the graph and what this means for the solution.

2 marksstandard

Quick Recall Flashcards

Intersection Point
The point where two graphs cross - this gives x and y values that satisfy both equations
Graphical Solution
Finding where two graphs intersect gives the solution to simultaneous equations

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