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2.7 Two-Variable Inequalities

2.7 Two-Variable Inequalities. Graphing Linear Inequalities Graphing Absolute-Value Inequalities. 1) Graphing Linear Inequalities. The graph of a linear inequality is a region of the coordinate plane that is bounded by a line. 1) Graphing Linear Inequalities. What it shows…

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2.7 Two-Variable Inequalities

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  1. 2.7 Two-Variable Inequalities Graphing Linear Inequalities Graphing Absolute-Value Inequalities

  2. 1) Graphing Linear Inequalities • The graph of a linear inequality is a region of the coordinate plane that is bounded by a line

  3. 1) Graphing Linear Inequalities • What it shows… • the values on the coordinate plane that apply to the function • What an equation looks like…

  4. 1) Graphing Linear Inequalities • What it shows… • the values on the coordinate plane that apply to the function • What an equation looks like… • Inequality symbol • Slope • y-intercept

  5. 1) Graphing Linear Inequalities • What linear inequality graphs look like… 1)boundary line (solid or dashed) 2)shaded area (above or below the boundary line)

  6. 1) Graphing Linear Inequalities A dashed boundary line means the line is NOT part of the solution The shading is ABOVE the boundary line if the equation is of the form y > OR y> y < OR y >

  7. 1) Graphing Linear Inequalities A solid boundary line means the line ISpart of the solution The shading is BELOW the boundary line if the equation is of the form y < OR y < y < OR y >

  8. 1) Graphing Linear Inequalities Example 1: Graph the inequality y< 2x + 2

  9. 1) Graphing Linear Inequalities Remember… y = mx + b Example 1: Graph the inequality y< 2x + 2

  10. 1) Graphing Linear Inequalities Remember… y = mx + b Example 1: Graph the inequality y< 2x + 2 y-int = 2 m = 2

  11. 1) Graphing Linear Inequalities Example 1: Graph the inequality y< 2x + 2 y-int = 2 m = 2

  12. 1) Graphing Linear Inequalities Example 1: Graph the inequality y< 2x + 2 y-int = 2 m = 2

  13. 1) Graphing Linear Inequalities Example 1: Graph the inequality y< 2x + 2 y-int = 2 m = 2

  14. 1) Graphing Linear Inequalities Example 1: Graph the inequality y< 2x + 2 y-int = 2 m = 2 y < DASHED line

  15. 1) Graphing Linear Inequalities Example 1: Graph the inequality y< 2x + 2 y-int = 2 m = 2 y < SHADE BELOW the line

  16. 1) Graphing Linear Inequalities Example 2: Write an inequality for the graph below.

  17. 1) Graphing Linear Inequalities Example 2: Write an inequality for the graph below. y = mx + b y –int = m = inequality type

  18. 1) Graphing Linear Inequalities Example 2: Write an inequality for the graph below. y = mx + b y –int = m = inequality type

  19. 1) Graphing Linear Inequalities Example 2: Write an inequality for the graph below. y = mx + b y –int = -3 m = inequality type

  20. 1) Graphing Linear Inequalities Example 2: Write an inequality for the graph below. y = mx + b y –int = -3 m = -3/2 inequality type >

  21. 1) Graphing Linear Inequalities Example 2: Write an inequality for the graph below. y –int = -3 m = -3/2 inequality type > Sub into y>mx + b

  22. 1) Graphing Linear Inequalities Example 2: Write an inequality for the graph below. y –int = -3 m = -3/2 inequality type > Sub into y>mx + b y > -3x/2- 3

  23. Homework • p.104 #1, 5, 7, 20, 21, 23, 26, 37, 38 Don’t forget… Quiz TUESDAY Test FRIDAY

  24. 2) Absolute Value Inequalities • Graph the absolute value function then shade above OR below

  25. 2) Absolute Value Inequalities • Graph the absolute value function then shade above OR below Solid line…y<, y> Dashed line…y<, y> Shade above y>, y> Shade below…y<, y<

  26. 2) Absolute Value Inequalities Example 1: Graph y< |x – 2| + 3

  27. 2) Absolute Value Inequalities Example 1: Graph y< |x – 2| + 3 DASHED line Shade BELOW slope = 1 Vertex = (2, 3)

  28. 2) Absolute Value Inequalities Example 1: Graph y< |x – 2| + 3 slope = 1 DASHED line Shade BELOW Vertex = (2, 3)

  29. 2) Absolute Value Inequalities Example 1: Graph y< |x – 2| + 3 slope = 1 DASHED line Shade BELOW Vertex = (2, 3)

  30. 2) Absolute Value Inequalities Example 1: Graph y< |x – 2| + 3 slope = 1 DASHED line Shade BELOW Vertex = (2, 3)

  31. 2) Absolute Value Inequalities Example 1: Graph y< |x – 2| + 3 slope = 1 DASHED line Shade BELOW Vertex = (2, 3)

  32. 2) Absolute Value Inequalities Example 1: Graph y< |x – 2| + 3 slope = 1 DASHED line Shade BELOW Vertex = (2, 3)

  33. 2) Absolute Value Inequalities Example 2: Graph –y + 1 < -2|x + 2|

  34. 2) Absolute Value Inequalities Example 2: Graph –y + 1 < -2|x + 2| -y< -2|x + 2| - 1 y> 2|x + 2| + 1 -y so CHANGE the direction of the inequality

  35. 2) Absolute Value Inequalities y> 2|x + 2| + 1

  36. 2) Absolute Value Inequalities y> 2|x + 2| + 1 Slope = 2 Solid line Shade above Vertex = (-2, 1)

  37. 2) Absolute Value Inequalities y> 2|x + 2| + 1

  38. 2) Absolute Value Inequalities y> 2|x + 2| + 1

  39. 2) Absolute Value Inequalities y> 2|x + 2| + 1

  40. 2) Absolute Value Inequalities y> 2|x + 2| + 1

  41. 2) Absolute Value Inequalities Example 3: Write an equation for the graph below.

  42. Homework p.104 #11-13, 22, 30, 39-42 Reminders… Quiz TUESDAY (2.5, 2.6, first half 2.7) Review WEDNESDAY, THURSDAY Test FRIDAY (Chapter 2 ONLY) Extra-help WEDNESDAY at LUNCH

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