🎯 Learning Objectives
- Draw boundary lines accurately.
- Choose solid or broken boundaries.
- Test a point to identify the correct region.
Introduction
This lesson develops Graphical Inequalities from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
🤔 Start with an Idea
An equation such as y = 2x + 1 draws a line. An inequality such as y > 2x + 1 describes an entire region on one side of that line.
📖 Key Notes
- Use a solid line for ≤ or ≥ because the boundary is included.
- Use a broken line for < or > because the boundary is excluded.
- Test a convenient point, often (0,0), unless it lies on the boundary.
🗺️ Shade the Correct Side
Represent y > x + 1.
🧠 Let's Think Together
Represent: y ≤ 2x + 3.
- Draw y = 2x + 3 as a solid line.
- Test (0,0): 0 ≤ 3 is true.
- Shade the side containing (0,0).
✍️ Worked Examples
x ≥ 2 uses the solid vertical line x = 2 and shading to the right.
y < 4 uses the broken horizontal line y = 4 and shading below.
🎯 Practice Questions
Easy
What boundary style is used for y < 3x − 1?
Show answer
A broken line.
Medium
Does (0,0) satisfy y ≥ x − 2?
Show answer
Yes, because 0 ≥ −2.
⚠️ Common Mistakes
- Shading before testing a point.
- Using the wrong line style.
- Treating x = a as a horizontal line.
📝 Exam Focus
Label each boundary and show a clear key or shading. In multiple-inequality questions, the required answer is the common feasible region.
Summary
- Draw the boundary equation.
- Choose solid or broken.
- Test a point.
- Shade the true side.