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# 1.7 linear inequalities

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### 1.7 linear inequalities

1. 1. 1.7 Linear Inequalities
2. 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. 3. Checking Solutions • Is (0, 1) a solution of 2x + 3y  5 ?
4. 4. You Try! • Is (4, -1) a solution of 2x + 3y  5 ? • Is (-3, 2) ?
5. 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. 6. Example: • Graph: y  -2
7. 7. • Graph: x  1
8. 8. You Try! • Graph the inequalities: y  2 x > 1 stop
9. 9. Two Variable Inequalities • Graph y < 2x - 3
10. 10. You Try! • Graph y > - x – 4
11. 11. Example: • Graph 2x – 5y ≥ 10 • Hint: Solve for y first.
12. 12. Your Turn! • Graph 4x + 2y ≥ 8
13. 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. 14. Example 1
15. 15. Example 2
16. 16. You Try!
17. 17. Example 3
18. 18. You Try!