3 5 graphing linear inequalities in two variables

688 views
434 views

Published on

Published in: Education, Technology, Business
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
688
On SlideShare
0
From Embeds
0
Number of Embeds
12
Actions
Shares
0
Downloads
50
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

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

×