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 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 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… 1. y < -2
Graph These… 2. -1 ≤ x + y
Graph These… 3. x > 4
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. 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 2 x + 4 y ≤ 12
Wrap Up Graphing Inequalities l Solid line/Dotted line l Shading HW: P. 305 #1 -23 odd; P. 308 #1 -4 all Write DLUQ for notes.
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