This document discusses linear inequalities and how to graph them. It introduces linear inequalities as expressions with inequality symbols like <, >, ≥, or ≤ instead of equals signs. Solutions to inequalities are ordered pairs that make the statement true. It explains how to check if a point is a solution, and how to graph inequalities by treating them as equalities and shading the correct side based on the inequality symbol and a test point. The document contains examples of graphing various one-variable and two-variable inequalities.

1. 1.7 Linear Inequalities

2. Linear Inequalities
• Look like the equation of a line, but
have , , , or  instead of =.
• Solutions are ordered pairs (x, y) that
make the inequality true.

3. Checking Solutions
• Is (0, 1) a solution of 2x + 3y  5 ?

4. You Try!
• Is (4, -1) a solution of 2x + 3y  5 ?
• Is (-3, 2) ?

5. Graphing Linear Inequalities
•Pretend the inequality is an = sign.
•Graph the line like normal except:
▫ < and > use dashed line
▫  and  use solid line
•Pick a point and plug it in to decide
where to shade.
•Shade the side that is TRUE!

6. Example:
• Graph: y  -2

7. • Graph: x  1

8. You Try!
• Graph the inequalities:
y  2 x > 1
stop

9. Two Variable Inequalities
• Graph y < 2x - 3

10. You Try!
• Graph y > - x – 4

11. Example:
• Graph 2x – 5y ≥ 10
• Hint: Solve for y first.

12. Your Turn!
• Graph 4x + 2y ≥ 8

13. Writing Inequalities from Graphs
1. Write the equation of the line.
Use y = mx + b if possible.
2. Choose a point (x, y) from the
shaded area and plug it in.
3. Replace = sign with an inequality
that makes the statement true.
4. For dashed lines choose < or >,
for solid lines choose  or .

14. Example 1

15. Example 2

16. You Try!

17. Example 3

18. You Try!