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2.8 – Graphing Inequalities

2.8 – Graphing Inequalities. 2.8 – Graphing Inequalities. Steps for graphing inequalities:. 2.8 – Graphing Inequalities. Steps for graphing inequalities: Graph just like you would an equation:. 2.8 – Graphing Inequalities. Steps for graphing inequalities:

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2.8 – Graphing Inequalities

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  1. 2.8 – Graphing Inequalities

  2. 2.8 – Graphing Inequalities Steps for graphing inequalities:

  3. 2.8 – Graphing Inequalities Steps for graphing inequalities: • Graph just like you would an equation:

  4. 2.8 – Graphing Inequalities Steps for graphing inequalities: • Graph just like you would an equation: • Table

  5. 2.8 – Graphing Inequalities Steps for graphing inequalities: • Graph just like you would an equation: • Table – used when eq. In slope-int. form

  6. 2.8 – Graphing Inequalities Steps for graphing inequalities: • Graph just like you would an equation: • Table – used when eq. In slope-int. form • x and y intercepts

  7. 2.8 – Graphing Inequalities Steps for graphing inequalities: • Graph just like you would an equation: • Table – used when eq. In slope-int. form • x and y intercepts – used when in standard form

  8. 2.8 – Graphing Inequalities Steps for graphing inequalities: • Graph just like you would an equation: • Table – used when eq. In slope-int. form • x and y intercepts – used when in standard form • If ≥ or ≤, make the line solid.

  9. 2.8 – Graphing Inequalities Steps for graphing inequalities: • Graph just like you would an equation: • Table – used when eq. In slope-int. form • x and y intercepts – used when in standard form • If ≥ or ≤, make the line solid. • If > or <, make the line dashed.

  10. 2.8 – Graphing Inequalities Steps for graphing inequalities: • Graph just like you would an equation: • Table – used when eq. In slope-int. form • x and y intercepts – used when in standard form • If ≥ or ≤, make the line solid. • If > or <, make the line dashed. • Plug the origin (0,0) into the inequality.

  11. 2.8 – Graphing Inequalities Steps for graphing inequalities: • Graph just like you would an equation: • Table – used when eq. In slope-int. form • x and y intercepts – used when in standard form • If ≥ or ≤, make the line solid. • If > or <, make the line dashed. • Plug the origin (0,0) into the inequality. • Plug 0 in for x and plug 0 in for y!

  12. 2.8 – Graphing Inequalities Steps for graphing inequalities: • Graph just like you would an equation: • Table – used when eq. In slope-int. form • x and y intercepts – used when in standard form • If ≥ or ≤, make the line solid. • If > or <, make the line dashed. • Plug the origin (0,0) into the inequality. • Plug 0 in for xand plug 0 in for y!

  13. 2.8 – Graphing Inequalities Steps for graphing inequalities: • Graph just like you would an equation: • Table – used when eq. In slope-int. form • x and y intercepts – used when in standard form • If ≥ or ≤, make the line solid. • If > or <, make the line dashed. • Plug the origin (0,0) into the inequality. • Plug 0 in for xand plug 0 in for y! • If true, shade side of line with the origin.

  14. 2.8 – Graphing Inequalities Steps for graphing inequalities: • Graph just like you would an equation: • Table – used when eq. In slope-int. form • x and y intercepts – used when in standard form • If ≥ or ≤, make the line solid. • If > or <, make the line dashed. • Plug the origin (0,0) into the inequality. • Plug 0 in for xand plug 0 in for y! • If true, shade side of line with the origin.

  15. 2.8 – Graphing Inequalities Steps for graphing inequalities: • Graph just like you would an equation: • Table – used when eq. In slope-int. form • x and y intercepts – used when in standard form • If ≥ or ≤, make the line solid. • If > or <, make the line dashed. • Plug the origin (0,0) into the inequality. • Plug 0 in for xand plug 0 in for y! • If true, shade side of line with the origin. • If false, shade side of line w/o the origin.

  16. 2.8 – Graphing Inequalities Steps for graphing inequalities: • Graph just like you would an equation: • Table – used when eq. In slope-int. form • x and y intercepts – used when in standard form • If ≥ or ≤, make the line solid. • If > or <, make the line dashed. • Plug the origin (0,0) into the inequality. • Plug 0 in for xand plug 0 in for y! • If true, shade side of line with the origin. • If false, shade side of line w/o the origin.

  17. Ex. 1 Graph 2x + 3y > 6

  18. Ex. 1 Graph 2x + 3y > 6 • Graph just like the equation:

  19. Ex. 1 Graph 2x + 3y > 6 • Graph just like the equation: So, graph 2x + 3y = 6

  20. Ex. 1 Graph 2x + 3y > 6 • Graph just like the equation: So, graph 2x + 3y = 6 x-int:

  21. Ex. 1 Graph 2x + 3y > 6 • Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0)

  22. Ex. 1 Graph 2x + 3y > 6 • Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int:

  23. Ex. 1 Graph 2x + 3y > 6 • Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2)

  24. Ex. 1 Graph 2x + 3y > 6 • Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2)

  25. Ex. 1 Graph 2x + 3y > 6 • Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2)

  26. Ex. 1 Graph 2x + 3y > 6 • Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) • If ≥ or ≤, make the line solid.

  27. Ex. 1 Graph 2x + 3y > 6 • Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) • If ≥ or ≤, make the line solid. • If > or <, make the line dashed.

  28. Ex. 1 Graph 2x + 3y > 6 • Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) • If ≥ or ≤, make the line solid. • If > or <, make the line dashed.

  29. Ex. 1 Graph 2x + 3y > 6 • Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) • If ≥ or ≤, make the line solid. • If > or <, make the line dashed.

  30. Ex. 1 Graph 2x + 3y > 6 • Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) • If ≥ or ≤, make the line solid. • If > or <, make the line dashed. • Plug the origin (0,0) into the inequality.

  31. Ex. 1 Graph 2x + 3y > 6 • Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) • If ≥ or ≤, make the line solid. • If > or <, make the line dashed. • Plug the origin (0,0) into the inequality. Plug 0 in for xand plug 0 in for y!

  32. Ex. 1 Graph 2x + 3y > 6 • Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) • If ≥ or ≤, make the line solid. • If > or <, make the line dashed. • Plug the origin (0,0) into the inequality. Plug 0 in for xand plug 0 in for y! 2(0) + 3(0) > 6

  33. Ex. 1 Graph 2x + 3y > 6 • Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) • If ≥ or ≤, make the line solid. • If > or <, make the line dashed. • Plug the origin (0,0) into the inequality. Plug 0 in for xand plug 0 in for y! 2(0) + 3(0) > 6 0 > 6

  34. Ex. 1 Graph 2x + 3y > 6 • Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) • If ≥ or ≤, make the line solid. • If > or <, make the line dashed. • Plug the origin (0,0) into the inequality. Plug 0 in for xand plug 0 in for y! 2(0) + 3(0) > 6 0 > 6 If true, shade side of line with the origin.

  35. Ex. 1 Graph 2x + 3y > 6 • Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) • If ≥ or ≤, make the line solid. • If > or <, make the line dashed. • Plug the origin (0,0) into the inequality. Plug 0 in for xand plug 0 in for y! 2(0) + 3(0) > 6 0 > 6 If true, shade side of line with the origin. If false, shade side of line w/o the origin.

  36. Ex. 1 Graph 2x + 3y > 6 • Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) • If ≥ or ≤, make the line solid. • If > or <, make the line dashed. • Plug the origin (0,0) into the inequality. Plug 0 in for xand plug 0 in for y! 2(0) + 3(0) > 6 0 > 6 If true, shade side of line with the origin. If false, shade side of line w/o the origin.

  37. Ex. 2 Graph y≤ x + 1

  38. Ex. 2 Graph y≤ x + 1 • Graph y = x + 1

  39. Ex. 2 Graph y≤ x + 1 • Graph y = x + 1

  40. Ex. 2 Graph y≤ x + 1 • Graph y = x + 1

  41. Ex. 2 Graph y≤ x + 1 • Graph y = x + 1 • y≤x + 1, so use solid line!

  42. Ex. 2 Graph y≤ x + 1 • Graph y = x + 1 • y≤x + 1, so use solid line!

  43. Ex. 2 Graph y≤ x + 1 • Graph y = x + 1 • y≤x + 1, so use solid line! • Plug in the origin: 0 ≤ 0 + 1 0 ≤ 1, TRUE!

  44. Ex. 2 Graph y≤ x + 1 • Graph y = x + 1 • y≤x + 1, so use solid line! • Plug in the origin: 0 ≤ 0 + 1 0 ≤ 1, TRUE!

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