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Warm Up # 1

Warm Up # 1. The perimeter of a rectangle is 32. The length is 1 more than twic e the width. What are the dimensions of the rectangle? Solve the system: . Homework Check . Essential Question. How can we represent the solution to a system of linear inequalities?. Graphing Linear

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Warm Up # 1

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  1. Warm Up # 1 • The perimeter of a rectangle is 32. The length is 1 more than twice the width. What are the dimensions of the rectangle? • Solve the system:

  2. Homework Check

  3. Essential Question How can we represent the solution to a system of linear inequalities?

  4. Graphing Linear Inequalities

  5. We show the solution to a linear inequality with a graph. Step 1) Put the inequalities into slope-intercept form. y = mx + b slope y-intercept

  6. Step 2) Graph the line • If the inequality is < or >, make the lines dotted. • If the inequality is < or >, make the lines solid.

  7. Step 3) Shade the correct region of the graph: • Above the line b) Below the line for y > or y . for y < or y ≤. **This is because more then 1 ordered pair can be a solution!

  8. Examples: 1) y > -5x + 4

  9. Examples: 2) x < 4 3) y ≥ -3

  10. Systems of Inequalities

  11. We show the solution to a system of linear inequalities with a graph!

  12. Steps to Graphing a System of Inequalities: • Put the inequalities into slope-intercept form. • Decide if the lines should be dotted or solid • Shade above for y > or y , shade below for y < or y ≤. • Shade the overlapping section darker to show where the solutions to both inequalities lie.

  13. Example #1: a: 3x + 4y > - 4 b: x + 2y < 2 Put in Slope-Intercept Form:

  14. Example, continued: a: dotted shade above b: dotted shade below Graph each line, make dotted or solid and shade the correct area.

  15. #2 Graph the system of linear inequalities. x³ –1 y> x – 2

  16. #3x > -2y < 6-2x + y > -5

  17. #4 y ≥ -x + 4y < 3x - 2

  18. #5 x – y > 3 7x – y ≤ -3

  19. #6 7x + 2y < -10 -x + 2y ≤ 11

  20. Classwork: Solving Systems of Inequalities Worksheet Homework: Unit 7 TEST -

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