6 5 Linear Inequalities Overview Graphing Linear Inequalities

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6. 5 Linear Inequalities

6. 5 Linear Inequalities

Overview - - Graphing Linear Inequalities Solid or Dotted Which Side to Shade Writing

Overview - - Graphing Linear Inequalities Solid or Dotted Which Side to Shade Writing Inequalities from a graph

Graphing Linear Inequalities in Two Variables How would you graph the equation x +

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

= ≤ Graph x + y ≤ 3 Pick a point not on the

= ≤ 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!

= ≥ Graph x + y ≥ 3 What point do you want to

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

Solid or dashed? The lines can be graphed as a solid line or a

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 …

Graphing Linear Inequalities Steps: 1. Graph the equation (solve for y) 2. Draw a

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

Graph These… 1. y < -2

Graph These… 1. y < -2

Graph These… 2. -1 ≤ x + y

Graph These… 2. -1 ≤ x + y

Graph These… 3. x > 4

Graph These… 3. x > 4

Graph These… 4. x – 3 y ≤ 12

Graph These… 4. x – 3 y ≤ 12

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

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

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

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

Application 9. Suppose your budget for a party allows you to spend no more

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 2 x + 4 y ≤ 12