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. Use this page as part of a wider topic revision path rather than treating it as an isolated fact. It is section 4 of 10 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and 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 ✓
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 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.