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Objectives

7.5 Systems of Inequalities. Objectives. The learner will graph linear inequalities. NCSCOS. 4.03. 7.5 Systems of Inequalities. Graphing a Linear Inequality in the Coordinate Plane 1. Graph the related linear equation. Use a solid line for  or . Use a dashed line

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Objectives

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  1. 7.5 Systems of Inequalities Objectives • The learner will graph linear inequalities. NCSCOS • 4.03

  2. 7.5 Systems of Inequalities Graphing a Linear Inequality in the Coordinate Plane 1. Graph the related linear equation. • Use a solid line • for  or . • Use a dashed line • for < or >.

  3. 7.5 Systems of Inequalities • ymx + b • y< mx + b Shade the below the line: Shade above the line: • ymx + b • y> mx + b

  4. 7.5 Systems of Inequalities • x c • x < c Shade left of the line: Shade right of the line: • x c • x> c

  5. 7.5 Systems of Inequalities Summary for Graphing Linear Inequalities 1. Solve for y = mx + b 2. Remember: change the symbol if you multiply or divide by a negative number. 3. Draw the boundary line (solid or dashed). 4. Shade the solution region (above or below,left or right).

  6. 7.5 System of Inequalities Graph the inequality: 1 2 y  x – 2

  7. 7.5 System of Inequalities Graph the inequality: y  3x – 2

  8. 7.5 System of Inequalities Graph the inequality: 2x – y  -3 –y  –2x – 3 y  2x + 3

  9. 7.5 System of Inequalities Graph the inequality: 73 23 y  x +

  10. 7.5 System of Inequalities Graph the inequality: 2x + 3y  6 3y  –2x + 6 23 y  - x + 2

  11. y > –x + 3 y x + 2 7.5 Systems of Inequalities Graph the inequalities:

  12. y – x – 1 y x + 3 7.5 Systems of Inequalities Graph the inequalities: 12

  13. y x – 3 y < – 2x + 1 7.5 Systems of Inequalities Graph the inequalities: 34

  14. 3x – y –2 x – y –1 7.5 Systems of Inequalities Graph the inequalities: y  3x + 2 y  x + 1

  15. y –4x + 7 y –2x – 6 7.5 Systems of Inequalities Graph the inequalities:

  16. y <3x + 1 y < -x + 5 7.5 Systems of Inequalities Graph the inequalities:

  17. y < – x + 1 y > 2x – 7 7.5 Systems of Inequalities Graph the inequalities: 1 5

  18. y >2x + 2 y > -x – 1 7.5 Systems of Inequalities Graph the inequalities:

  19. y < -2x y > – x – 3 7.5 Systems of Inequalities Graph the inequalities: 1 2

  20. 3x + y < 4 x – 2y < 6 7.5 Systems of Inequalities Graph the inequalities: y < -3x + 4 1 2 y > x – 3

  21. -2x + y < 3 3x – y > -5 7.5 Systems of Inequalities Graph the inequalities: y < 2x + 3 y < 3x + 5

  22. 7.5 Systems of Inequalities During the summer, Kara wants to earn at least $126 per week by working part-time. She can make $6 an hour doing yard work and $7 an hour working at the library. She can work no more than 30 hours each week. Write a system of inequalities to represent Kara’s situation, and then graph the results.

  23. 7.5 Systems of Inequalities Graph the inequalities: 40 y  –x + 30 30 76 y  - x + 21 20 10 The intersection of the green area will meet both of Kara’s needs. 2 4 6 8 10 12 14

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