Worked Example 4: Linear Inequality

Part of Graphical Solutions · Section 8 of 10

Study NotesUnit: AlgebraGCSE

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. 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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