Graphical Inequalities | Mathematics for GCSE/IGCSE - Year 11 PDF Download

Finding Regions using Inequalities

How to represent inequalities graphically?

• Start by understanding Linear Graphs

To graph an inequality;

• Draw the line using "=". Use a solid line for ≤ or ≥ to indicate that the line is included. Use a dotted line for < or > to indicate that the line is not included.
• Decide which side of the line is wanted:
  • Below the line if "y ≤ ..." or "y < ...".
  • Above the line if "y ≥ ..." or "y > ...".
  • Use a point that's not on the line as a test if unsure. Substitute its x and y value into the inequality to examine whether the inequality holds true on that side of the line.
• Shade the unwanted side of each line, unless the question says otherwise. 
  • This is because it is easier to see which region has not been shaded than it is to look for a region that has been shaded multiple times.
  • Graphing software often shades the area that is required, but this can be overcome by reversing the inequality sign.

Interpreting Graphical Inequalities

How do we interpret inequalities on a graph?

• Begin by examining linear graphs.

When interpreting inequalities and finding regions defined by them with linear graphs:

• Write down the equation of each line on the graph.
• Remember to draw lines with:
  • A solid line for ≤ or ≥ to indicate that the line is included in the region.
  • A dotted line for < or > to indicate that the line is not included.
• Replace the = sign with:
  • ≤ or < if shading below the line.
  • ≥ or > if shading above the line.
  • Use a point to test if unsure about which side of the line to shade.