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Graphing Lines and Linear Inequalities

Graphing Lines and Linear Inequalities. Linear Inequalities. Linear Equations. Drive on The Education Highway. Linear Equations and Graphing 1. Parts of a Coordinate Plane 2. Slope 3. Slope-intercept Form of a Linear Equation 4. Graphing by x- & y-intercepts.

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Graphing Lines and Linear Inequalities

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  1. Graphing Lines and Linear Inequalities Linear Inequalities Linear Equations Drive on The Education Highway

  2. Linear Equations and Graphing 1. Parts of a Coordinate Plane 2. Slope 3. Slope-intercept Form of a Linear Equation 4. Graphing by x- & y-intercepts.

  3. Parts of a coordinate plane.

  4. Click on the correct quadrant numbers. Correct answer = applause. 6 5 Quadrant Quadrant 4 I II III IV I II III IV 3 2 1 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1 Quadrant Quadrant -2 -3 I II III IV I II III IV -4 -5 -6 Lesson Start

  5. Click on the correct axis names. Correct answer = clapping. 6 5 4 3 2 1 x-axis y-axis -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 x-axis y-axis Lesson Start

  6. Click on the point for the origin. Correct answer = clapping. 6 5 4 3 2 1 x -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 Lesson Start y

  7. Click on point (-3, 5). Correct point = applause. 6 5 4 3 2 1 x -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 Lesson Start y

  8. You chose a line segment instead of a point. Go back and try again. INCORRECT ANSWER

  9. You chose point (5, -3). Each ordered pair is in the form (x, y) -- it follows the alphabet in its internal order. You find the x value first, then you find the y value. Where they meet is the point. Go back and try again. INCORRECT ANSWER

  10. Click on the correct ordered pair for the black point. 6 5 4 3 2 1 x -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1 -2 -5/4 (-5, 4) -3 (4, -5) -4/5 -4 -5 -6 Lesson Start y

  11. You did not choose an ordered pair. Go back and try again. INCORRECT ANSWER

  12. You chose the ordered pair for the pale green point. Remember: x comes before y in the alphabet and in an ordered pair. Go back and try again. INCORRECT ANSWER

  13. Return to Main Menu. Return to Prior Problem. Continue to Next Lesson.

  14. Slopes 1. What is a slope? 2. Slope formula 3. Types of slopes

  15. What is slope? Slope is the slant of a line. Slope = risechange in y’s run change in x’s Slope is a fraction/integer. Lesson Start

  16. How to determine the slope when the line goes up. 1. Count the number of units up from the right point to the left point. 5 4 9 1 2 3 4 5 6 7 8 6 3 5 2 4 1 3 x -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 2 2. Put that number on top of the fraction line. -1 Slope= 6 1 -2 9 -3 -4 3, Count the number of units to the right. 4. Put that number under the fraction line. y Lesson Start

  17. How to determine the slope when the line goes down. 1. Count the number of units down from right point to left point. 5 4 -1 3 -2 2 -3 1 -4 x 2. Put that number on top of fraction line. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -5 -1 Slope = -6 -6 2 1 3 -2 3 -3 -4 3. Count the units to the right. y 4. Put that number under the fraction line. Lesson Start

  18. Determine the slope of the line shown. 5 4 3 2 1 x -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1 -2 -3 -4 -1/3 3/1 y -3/1 1/3 Lesson Start

  19. The line does not go down. Go back and try again. INCORRECT ANSWER Lesson Start

  20. The line does not rise 3 units, then run 1 unit to the right. Go back and try again. INCORRECT ANSWER Lesson Start

  21. Determine the slope of the line shown. 5 4 3 2 1 x -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1 -2 -3 -4 -2/3 3/2 y -3/2 2/3 Lesson Start

  22. The line does not go up. Go back and try again. INCORRECT ANSWER Lesson Start

  23. The line does not rise -2 units, then run 3 units to the right. Go back and try again. INCORRECT ANSWER Lesson Start

  24. Slope Formula: m = (y1 - y2) (x1 - x2) where m = slope and (x1, y1), (x2, y2) are points on the line. Lesson Start

  25. Example: Find the slope for a line with points (-3, 4) and (7, -2) on it. 1. Assign values as follows: (x1, y1) = (-3, 4) (x2, y2) = (7, -2) 2. Substitute them into the formula and solve. m = 4 - (-2) = 6 = -3 -3 - 7 -10 5 Lesson Start

  26. Find the slope of the line with points (5, 6) and (2, 9) on it. 1. (x1, y1) = (5, 6) (2, 9) Lesson Start

  27. Find the slope of the line with points (5, 6) and (2, 9) on it. 1. (x1, y1) = (5, 6) 2. (x2, y2) = (5, 6) (2, 9) Lesson Start

  28. Find the slope of the line with points (5, 6) and (2, 9) on it. 1. (x1, y1) = (5, 6) 2. (x2, y2) = (2, 9) 6 + 9 5 + 2 6 - 9 5 - 2 3. m = 5 - 2 6 - 9 5 + 2 6 + 9 Lesson Start

  29. The slope formula is a case of subtraction on top and bottom. Go back and try again. INCORRECT ANSWER Lesson Start

  30. You have your x’s and y’s upside down. Remember: “Y’s guys are always in the skies!” Go back and try again. INCORRECT ANSWER Lesson Start

  31. You have your x’s and y’s upside down. You are also adding when you need to subtract. Go back and try again. INCORRECT ANSWER Lesson Start

  32. Find the slope of the line with points (5, 6) and (2, 9) on it. 1. (x1, y1) = (5, 6) 2. (x2, y2) = (2, 9) 3. m = 6 - 9 = -3 = -1 5 - 2 3 Lesson Start

  33. Find the slope of the line with points (7, 5) and (3, -4) on it. m = 5 - 4 = 1 7 - 3 4 7 - 3 = 4 5 - (-4) 9 5 - (-4) = 9 3 - 7 -4 5 - (-4) = 9 7 - 3 4 Lesson Start

  34. You have your x’s and y’s upside down. Remember: “Y’s guys are always in the skies!” Go back and try again. INCORRECT ANSWER Lesson Start

  35. It is not 5 - 4, it is 5 - (-4). Go back and try again. INCORRECT ANSWER Lesson Start

  36. You must start with the y and x from the first point and end with the y and x from the second point. Go back and try again. INCORRECT ANSWER Lesson Start

  37. Types of Slopes: 1. Positive and Negative Slopes 2. Special Types of Slopes 3. Determining Types of Slopes by Looking at Graphs of Lines 4. Determining Types of Slopes Algebraically. Lesson Start

  38. Positive and Negative Slopes. Type Graph Algebra Positive Up left to right. Positive Fraction SMILE Negative Down left to right. Negative Fraction Frown Lesson Start

  39. 2 Special Types of Slopes Type Graphs Algebra Zero Horizontal Line 0/a, a  0 Why, o y, do I look upon the horizon? Undefined Vertical Line a/0 No Slope Lesson Start

  40. Determining Types of Slopes by Looking at Graphs of Lines Lesson Start

  41. Is the slope of the line positive, negative, zero, or undefined? 5 4 3 2 1 x -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1 -2 -3 -4 + 0  - y Lesson Start

  42. Is the slope of the line positive, negative, zero, or undefined? 5 4 3 2 1 x -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1 -2 -3 -4 +  0 - y Lesson Start

  43. Is the slope of the line positive, negative, zero, or undefined? 5 4 3 2 1 x -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1 -2 -3 -4 + 0  - y Lesson Start

  44. Is the slope of the line positive, negative, zero, or undefined? 5 4 3 2 1 x -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1 -2 -3 -4 + 0  - y Lesson Start

  45. Click on the line with the negative slope. 5 4 3 2 1 x -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1 -2 -3 -4 y Lesson Start

  46. Click on the line with the zero slope. 5 4 3 2 1 x -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1 -2 -3 -4 y Lesson Start

  47. Click on the line with the no slope. 5 4 3 2 1 x -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1 -2 -3 -4 y Lesson Start

  48. Click on the line with the positive slope. 5 4 3 2 1 x -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1 -2 -3 -4 y Lesson Start

  49. Determining Types of Slopes Algebraically. Lesson Start

  50. Is the slope of the line with the 2 points listed positive, negative, zero, or undefined? Points (-3, 5) and (-9, -4) + - 0  Lesson Start

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