Standard: SWBAT sketch the region defined by linear inequality 6.5 Linear Inequalities Standard: SWBAT sketch the region defined by linear inequality Chapter 6 Algebra 1 Ms. Mayer

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 + y = 3? x + y = 3 -x -x y = -x + 3 m = -1 b = 3 What happens if the “=“ changes to “≤” or “≥”? We get shading!!!

=  ≤ 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 pick?

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 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… y < -2

Graph These… 2. -1 ≤ x + y

Graph These… 3. x > 4

Graph These… 4. x – 3y ≤ 12

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

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 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

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