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6.5 Linear Inequalities

6.5 Linear Inequalities. Standard: SWBAT sketch the region defined by linear inequality. Mini Quiz 53. 1. Determine if 5 is a solution to 2. Graph the equation y = x – 2. Overview. Graphing Linear Inequalities Solid or Dotted Which Side to Shade Writing Inequalities from a graph.

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6.5 Linear Inequalities

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  1. 6.5 Linear Inequalities Standard: SWBAT sketch the region defined by linear inequality

  2. Mini Quiz 53 1. Determine if 5 is a solution to 2. Graph the equation y = x – 2

  3. Overview • Graphing Linear Inequalities • Solid or Dotted • Which Side to Shade • Writing Inequalities from a graph

  4. Graphing Linear Inequalities in Two Variables How would you graph the equation x + y = 3? x + y = 3 -x -x y = -x + 3 m = -1 b = 3 What happens if the “=“ changes to “≤” or “≥”? We get shading!!!

  5. =  ≤ Graph x + y ≤ 3 Pick a point not on the line to find out which side to shade. If it’s true, shade same side. If not, shade the opposite side!

  6. =  ≥ Graph x + y ≥ 3 What point do you want to pick?

  7. Solid or dashed? The lines can be graphed as a solid line or a dashed (dotted) line. When do you think it’s solid, and when is it dashed? Think about graphing points on a number line; when is it open and when is it closed? < or > is … ≤ or ≥ is …

  8. Graphing Linear Inequalities Steps: 1. Graph the equation (solve for y) 2. Draw a Dotted or Solid line 3. Pick a point not on a line (any point) 4. Shade the correct side • True – shade the same side • False – shade the opposite side

  9. Graph These… • y < -2

  10. Graph These… 2. -1 ≤ x + y

  11. Graph These… 3. x > 4

  12. Graph These… 4. x – 3y ≤ 12

  13. Writing an Inequality Write an inequality for each graph. 5. 6.

  14. Writing an Inequality Write an inequality for each graph. 7. 8.

  15. Application 9. Suppose your budget for a party allows you to spend no more than $12 on peanuts and cashews. Peanuts cost $2/lb and cashews cost $4/lb. Find three possible combinations of peanuts and cashews you can buy. x = number of pounds of peanuts y = number of pounds of cashews 2x + 4y ≤ 12

  16. Wrap Up Graphing Inequalities • Solid line/Dotted line • Shading HW: P. 305 #1-23 odd; P. 308 #1-4 all Write DLUQ for notes.

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