1. Linear inequalities You know how to graph expressions like these:

2. Today we’ll expand that to expressions like …. y < 3x – 1
Today we’ll expand that to expressions like … y < 3x – If you can graph a line, you can graph an inequality.

3. To graph: •. Find the associated line. (think what it would be if it
To graph: • Find the associated line (think what it would be if it said = instead of < or >)

4. •. If < or >, graph a dotted. line •
• If < or >, graph a dotted line • If < or >, graph a solid line.

5. • If < or <, shade below the line.

6. • Of > or >, shade above the line.

7. Graph y < 2x - 4

8. Graph y < 2x - 4

9. Graph y < -x + 1

10. Graph y < -x + 1

11. Graph y > -½ x – 3

12. Graph y > -½ x – 3

13. What inequalities are graphed?

14. What inequalities are graphed? y < -2/3x + 6

16. y > x + 1

17. If the line is not in slope/intercept form, you can tell which side to shade by picking a point on one side and seeing if it works in the expression.

18. For example … x + 2y < 8 . You could graph with the
For example … x + 2y < 8  You could graph with the intercepts (8,0) and (0,4).  It will be a dotted line.

19. x + 2y < 8 Pick a point not on the line (like (0,0) … the easiest point possible) 0 < 8 Since this works, we shade in the direction of (0,0).

20. x + 2y < 8 Here’s the final answer:

21. x + 2y < 8 If you had picked a point on the other side of the line (like (4,4), for instance) … 4 is NOT < 8 So you’d shade the other way.