7 5 Inequalities And Graphing

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7 5 Inequalities And Graphing

  1. 1. Inequalities and Graphing Chapter 7.4 Pages 345-349
  2. 2. Graph -6 -4 -2 0 +2 +4 +6
  3. 3. Graph’s Solution -6 -4 -2 0 +2 +4 +6
  4. 4. What’s the Deal? <ul><li>In this lesson We will review: </li></ul><ul><ul><li>graphing from y-intercept form and standard form. </li></ul></ul><ul><ul><li>balancing inequality equations. </li></ul></ul><ul><li>We will find that inequalities have an infinite number of solutions. </li></ul><ul><li>We will use dashed and solid lines for our equations. </li></ul>
  5. 5. Find the equation in y-intercept form then graph. <ul><li>2x + 3y = 6 </li></ul><ul><li>-2x -2x </li></ul><ul><li>3y= 6 - 2x </li></ul><ul><li>Then divide all terms by 3 </li></ul><ul><li>3y = 6 - 2x </li></ul><ul><li>3 3 </li></ul><ul><li>y= 2 – 2/3x </li></ul><ul><li>Rewrite: y = -2/3x +2 </li></ul><ul><li>Graph. </li></ul>
  6. 6. Find the same equation in y-intercept form with an inequality. <ul><li>2x + 3y < 6 </li></ul><ul><li>-2x -2x </li></ul><ul><li>3y< 6 - 2x </li></ul><ul><li>Then divide all terms by 3 </li></ul><ul><li>3y < 6 - 2x </li></ul><ul><li>3 3 </li></ul><ul><li>y< 2 – 2/3x </li></ul><ul><li>Rewrite: y < -2/3x + 2 </li></ul><ul><li>Graph with a dashed line (<). </li></ul><ul><li>This is similar to the open circle. </li></ul>
  7. 7. equation solutions. Now is where the fun begins. The x and y values of MANY points will make our equation correct. Actually, an infinite number of points will make our inequality correct.
  8. 8. Do the origin values make the equation correct? We use 2x + 3y < 6 Next: fill in (0,0) for x and y into the original equation. Is 2(0) + 3(0) < 6? 0+0 < 6
  9. 9. The origin is ONE coordinate from the many that work. If 2x + 3y < 6 Next: fill in another value on the same side as (0,0) Let’s pick (-1, -2) Is 2(-1) + 3(-2) < 6? -2 + -6 < 6
  10. 10. Many coordinates work. So we can graph them. If 2x + 3y < 6 All these values will work. We can show this by using shading or slanted lines. The dotted lines show that any point on the line makes the equation equal. And NOT part of this equation.
  11. 11. NOT a solution. We found 2x + 3y < 6 Use (3,0) 2(3) + 3(0) < 6 6+0 is NOT < 6 Graph everything down and to the left of the dashed line instead of graphing every point.
  12. 12. <ul><li>-2x + 3y < -15 </li></ul><ul><li>+2x +2x </li></ul><ul><li>3y < -15 + 2x </li></ul><ul><li>Divide all terms by 3 </li></ul><ul><li>3y < -15 + 2x </li></ul><ul><li>3 3 3 </li></ul><ul><li>y < -5 + 2/3x </li></ul><ul><li>Rewrite: y < + 2/3x - 5 </li></ul>Graph the inequality -2x + 3y < -15
  13. 13. <ul><li>Now try the values of the origin in the equation. </li></ul><ul><li>-2x + 3y < -15 </li></ul><ul><li>-2(0) + 3(0) < -15 </li></ul><ul><li>Is 0+0 < -15? </li></ul>Graph the inequality -2x + 3y < -15
  14. 14. <ul><li>Since (0,0) does NOT work, graph the opposite side of where the origin is found. </li></ul><ul><li>-2(0) + 3(0) < -15 </li></ul><ul><li>0+0 isn’t < -15? </li></ul>Graph the inequality -2x + 3y < -15
  15. 15. <ul><li>Graph with lines or shading. </li></ul>Show 0 + 0 is not < -15
  16. 16. Assignment pg. 351: 17 - 31 odds (Stay Tuned for part 2)
  17. 17. Graphing Inequalities Part Two
  18. 18. Warm-up <ul><li>Graph 3x - y > -2 </li></ul><ul><li>Solution on the next slide </li></ul>
  19. 19. Warm-up equation <ul><li>Graph 3x - y > -2 </li></ul><ul><li>-3x -3 x </li></ul><ul><li>-y > -2 – 3x </li></ul><ul><li>Divide all terms by -1 and switch the sign. </li></ul><ul><li>-y < -2 - 3 x </li></ul><ul><li>-1 -1 -1 </li></ul><ul><li>y < +1 + 3x OR </li></ul><ul><li>y < +3x + 1 </li></ul>
  20. 20. Warm-up answer <ul><li>Check 3x - y > -2 </li></ul><ul><li>with the origin (0,0) </li></ul><ul><li>3(0) – (0) > -2 </li></ul><ul><li>0>2 so the origin works. Shade right. </li></ul>
  21. 21. Let’s add another equation <ul><li>Graph </li></ul><ul><li>Slope is 0. (0x + 1) </li></ul><ul><li>Shade up. </li></ul>
  22. 22. What’s the solution? <ul><li>Graph </li></ul><ul><li>Where do the graphed lines from both equations meet? </li></ul>
  23. 23. Graph the inequalities Subtract x from both sides. z < -x + 3 Add x to both sides. z < +x + 3
  24. 24. Graph the inequalities Graph as if z is y. z < -1x + 3 Add x to both sides. z < +1x + 3 Fill in the values of the origin into both equations and shade. 0 + 0 < + 3 0 - 0 > + 3
  25. 25. Graph the inequalities 0 + 0 < + 3? yes 0 - 0 > + 3? No The solutions are found where the shading overlaps.
  26. 27. extras
  27. 28. Graphing

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