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Understanding Inequalities and Regions in Graphs

This module explores inequalities, showcasing the relationship between two variables (x and y). It provides examples such as y > 2x + 1 and y < x - 3. You'll learn how to read graphs to identify inequalities in specific regions and how to graph inequalities while shading the necessary areas. Key skills include drawing straight-line graphs and determining the shaded region based on selected points. This knowledge is essential for solving problems involving inequalities in various contexts, making it a valuable addition to your mathematical toolkit.

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Understanding Inequalities and Regions in Graphs

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  1. Inequalities & Regions OCR Module 8

  2. An inequality? • An INEQUALITY shows a relationship between two variables, usually x & y • Examples • y > 2x + 1 • y < x – 3 • 3x + 4y = 12

  3. What are you required to do? • Read a graph and write down the inequalities that contain a region • Draw inequalities and indicate the region they describe • You need to know how to plot straight line graphs [covered in Stage 7]

  4. y x For example X=2 x > 2 When dealing with ONE inequality, we SHADE IN the REQUIRED REGION

  5. y x For example X=-2 x < -2

  6. y x For example y < -1 y=-1

  7. y (1,2) x For example y= 2x+1 y < 2x +1 Which side is shaded? Pick a point NOT on line Is 2 < 2 x 1 + 1 ? YES (1,2) lies in the required region

  8. y (2,1) x For example y= 3x-2 y > 3x - 2 Which side is shaded? Pick a point NOT on line Is 1 > 3 x 2 - 2 ? NO (2,1) does NOT lie in the required region

  9. Drawing Inequalities Back to Stage 7

  10. y (2,1) x How to draw graph of equation y = 3x + 2 Shade IN the Region for y > 3x + 2 Is 1 > 3 x 2 + 2 ? NO (2,1) does NOT lie in the required region

  11. y (3,2) x How to draw graph of equation 4y + 3x = 12 Shade IN the Region for 4y + 3x > 12 Is 4 x 2 + 3 x 3 > 12 ? YES (3,2) DOES lie in the required region

  12. Exam Question An example

  13. (3,2) 2 < 3 ? y < 3 x + y = 4 x = 4 3 < 4 ? y = 3 x < 4 3 + 2 > 4 ? x + y > 4

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