Inequalities on Graphs (OCR A Level Maths: Pure)

Inequalities on graphs

• Inequalities can be represented on graphs by shaded regions and dotted or solid lines

• These inequalities have two variables, x and y
• Several inequalities are used at once
• The solution is an area on a graph (often called a region)
• The inequalities can be linear or quadratic

How do I draw inequalities on a graph?

• Sketch each graph
  • If the inequality is strict (< or >) then use a dotted line
  • If the inequality is weak (≤ or ≥) then use a solid line
• Decide which side of the line satisfies the inequality
  • Choose a coordinate on each side and test it in the inequality
    • The origin is an easy point to use
  • If it satisfies the inequality then that whole side of the line satisfies the inequality
    • For example: (0,0) satisfies the inequality y < x² + 1 so you want the side of the curve that contains the origin