This study notes covers Worked Example 4: Linear Inequality 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 8 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 4: Linear Inequality
Solve graphically: y ≥ 2x - 1
Step 1 Plot boundary line
y = 2x - 1 (solid line since ≥)
y-intercept: (0, -1)
Gradient: 2
Step 2 Test a point
Use origin (0, 0): Is 0 ≥ 2(0) - 1?
Is 0 ≥ -1? Yes! ✓
So shade the region containing origin
Step 3 Identify solution
Shade region above and including the line
Solution: All points on or above y = 2x - 1
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.