1. 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

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

3. 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!!!

4. =  ≤
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!

5. =  ≥
Graph x + y ≥ 3
What point do you want to pick?

6. 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 …

7. 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

8. Graph These…
y < -2

9. Graph These…
2. -1 ≤ x + y

10. Graph These…
3. x > 4

11. Graph These…
4. x – 3y ≤ 12

12. Writing an Inequality
Write an inequality for each graph.

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

14. 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

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