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# 3 5 graphing linear inequalities in two variables

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### 3 5 graphing linear inequalities in two variables

1. 1. 3.5 Graphing Linear Inequalities in Two Variables
2. 2. What is a Linear Inequality? • An inequality containing x and y whose boundary is a straight line.
3. 3. Checking Solutions • Solutions of linear inequalities are ordered pairs (x, y) that make the inequality true. • To check if a point is a solution: ▫ Plug it in for x and y ▫ Simplify ▫ Does it make a true statement?
4. 4. Example • Is (-1, 9) a solution of 2x + y < -3 ?
5. 5. Example • Is (2, -2) a solution of x – 3y ≥ 8 ?
6. 6. Example • Is (-3, 4) a solution of y > -1 ?
7. 7. Example • Is (0, 0) a solution of y > x ?
8. 8. You Try! • Is (-4, -1) a solution of 5x – 2y ≤ -1?
9. 9. Graphs of Linear Inequalities • Linear inequalities, like linear equations, cannot be “solved” to get a number answer. • Instead, we use a graph to show all solutions! • Graphs will contain a “boundary line” and a shaded “half plane.”
10. 10. Dashed or Solid • A dashed line means points on the line are not solutions. ▫ Use for < and >. • A solid line means points on the line are solutions. ▫ Use for ≤ and ≥.
11. 11. Where to Shade? • The shaded area shows all possible points that make the inequality true. • Test a point. ▫ We usually use (0,0). ▫ If it is on the line, choose a different point. • If it is a solution, shade that side. • If it is not a solution, shade the other side.
12. 12. Graphing Simple Linear Inequalities • Linear inequalities with only one variable have horizontal or vertical boundary lines. • x: vertical (up and down) • y: horizontal (side to side)
13. 13. Example: • Graph y ≤ 2.
14. 14. Example: • Graph x > 1.
15. 15. Example: • Graph y ≥ -5.
16. 16. You Try! Graph y > -1 Graph 3.5 > x
17. 17. Slope-Intercept Form • Remember: y = mx + b • m = slope ▫ rise over run! • (0, b) = y-intercept
18. 18. Example • Graph y ≤ 3x – 1
19. 19. Example • Graph y > ½ x + 3
20. 20. Example • Graph y ≥ - x – 2
21. 21. You Try! • Graph y < x + 2
22. 22. Standard Form • Remember: ax + by = c • Two choices: ▫ Solve for y. Rewrite as y = mx + b. - or ▫ Find intercepts: (0, y) and (x, 0)
23. 23. Graphing Practice/Review • Graph 3x + 2y = -6 both ways.
24. 24. Example • Graph –x + 2y > 2
25. 25. Example • Graph 3x – 2y < 6
26. 26. Example • Graph 3x – 2y ≥ 0
27. 27. You Try! • Graph –x + 4y > – 2