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Rewriting Equations 

Rewriting Equations . L esson E ssential Q uestion: How do you rewrite equations from standard form to graphing form?. 2 Forms of Linear Equations . The forms of linear equations are the formats in which the information is written in.

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Rewriting Equations 

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  1. Rewriting Equations  Lesson Essential Question: How do you rewrite equations from standard form to graphing form? Geometry CP

  2. 2 Forms of Linear Equations  • The forms of linear equations are the formats in which the information is written in. • These two forms are the most commonly used ways to write linear equations. 1. Standard Form: Ax + By =C 2. Slope InterceptForm: y=mx+b Geometry CP

  3. Important!!!  This is one of the BIG concepts you will need for high school. Slope – Intercept Form y = mx + b m represents the slope b represents the y-intercept Geometry CP

  4. Review: -Writing Equations Given Slope & Y-intercept Write the equation of a line that has a y-intercept of - 3 and a slope of - 4. y = -3x – 4 y = -4x – 3 y = -3x + 4 y = -4x + 3 Geometry CP

  5. Review: Find the slope and y-intercept of y = 4 – 2x m = 2; b = 4 m = 4; b = 2 m = -2; b = 4 m = 4; b = -2

  6. Standard Form to Slope Intercept Form Ax + By = C to y = mx + b

  7. Converting from standard form (Ax + By = C) to slope-intercept form (y = mx + b)

  8. WE WANT THIS FORM!!! 3 3 3 2 x y = 2 - 3 2 y = - + 2 x 3 Converting Standard to Slope-Intercept form 2x + 3y = 6 ax + by = c (Standard Form) -2x -2x 3y = 6 - 2x y = mx + b (Slope- Intercept)

  9. 3 Powerful Moves to get your equation into y= 6X + 4Y = 12 • MOVE X • DROP ALL • DIVIDE ALL Geometry CP

  10. 3 Powerful Moves to get your equation into y= 6X + 4Y = 12 6X + 4Y = 12 -6x -6x • MOVE X Add or Subtract the x term to the other side of equals. Geometry CP

  11. 3 Powerful Moves to get your equation into y= 6X + 4Y = 12 6X + 4Y = 12 -6x -6x 4y = 12 -6x 2. DROP ALL Bring all terms down in order. Do not add or subtract unlike terms!!! Geometry CP

  12. 3 Powerful Moves to get your equation into y= 6X + 4Y = 12 6X + 4Y = 12 -6x -6x 4y = 12 -6x 4 4 4 y= 3 – 3/2 x 3. DIVIDE ALL Divide each term by the number attached to y keep slope a fraction! Geometry CP

  13. 3 Powerful Moves to get your equation into y= -4X + 3Y = 12 • MOVE X • DROP ALL • DIVIDE ALL Geometry CP

  14. 3 Powerful Moves to get your equation into y= -4X + 3Y = 12 -4X + 3Y = 12 +4x +4x • MOVE X Add or Subtract the x term to the other side of equals. Geometry CP

  15. 3 Powerful Moves to get your equation into y= -4X + 3Y = 12 -4X + 3Y = 12 +4x +4x 3y = 12 +4x 2. DROP ALL Bring all terms down in order. Do not add or subtract unlike terms!!! Geometry CP

  16. 3 Powerful Moves to get your equation into y= -4X + 3Y = 12 -4X + 3Y = 12 +4x +4x 3y = 12 +4x 3 3 3 y= 4 + 4/3 x 3. DIVIDE ALL Divide each term by the number attached to y keep slope a fraction! Geometry CP

  17. The 3 Power Moves to getting linesinto y = form. MOVE the x term by Adding/Subtracting! 1. 2. 3. Drop ALL! Divide ALL! Geometry CP

  18. Pair Race Directions Equations are going to flash on the screen. The first one to step forward and describe the first step to converting the equation will earn the point. First person to answer correctly wins! Everyone….Please pay attention  Geometry CP

  19. Example 3x + 2y = 18 The first step is: Subtract 3x from both sides That would look like: 3x + 2y = 18 -3x -3x 2y = 18 – 3x Geometry CP

  20. Example -7x + 14y = 28 The first step is: Add 7x to both sides That would look like: -7x + 14y = 28 +7x +7x 14y = 28 + 7x Geometry CP

  21. Let’s Race! • As quickly and quietly as possible line up please! • No hitting, touching, pushing, poking…just get in line! Ready, Set, GO!! Geometry CP

  22. Correct! Subtract 4x from both sides!! Great Job! 4x + 5y = 10 4x + 5y = 10 -4x -4x 5y = 10 – 4x Geometry CP

  23. Correct! Add 6x to both sides!! Great Job! -6x + 3y = 12 -6x + 3y = 12 +6x +6x 3y = 12 + 6x Geometry CP

  24. Correct! Subtract 9x from both sides!! Great Job! 9x - y = -8 9x - y = -8 -9x -9x - y = -8 – 9x Geometry CP

  25. Correct! Subtract 10x from both sides!! Great Job! 10x - 20y = 20 10x - 20y = 20 -10x -10x -20y = 20 – 10x Geometry CP

  26. Correct! Add 11x to both sides!! Great Job! -11x + 11y = 33 -11x + 11y = 33 +11x +11x 11y = 33 + 11x Geometry CP

  27. Correct! Add 4x to both sides!! Great Job! -4x + 2y = 8 -4x + 2y = 8 +4x +4x 2y = 8 + 4x Geometry CP

  28. Correct! Add 8x to both sides!! Great Job! -8x - 4y = -16 -8x - 4y = -16 +8x +8x -4y = -16 + 8x Geometry CP

  29. Correct! Subtract 7x from both sides!! Great Job! 7x + y = -2 7x + y = -2 -7x -7x y = -2 – 7x Geometry CP

  30. Correct! Subtract 2x from both sides!! Great Job! 2x + 2y = 10 2x + 2y = 10 -2x -2x 2y = 10 – 2x Geometry CP

  31. Correct! Add 5x to both sides!! Great Job! -5x + 3y = -9 -5x + 3y = -9 +5x +5x 3y = -9 + 5x Geometry CP

  32. Correct! Add 8x to both sides!! Great Job! -8x - 4y = 24 -8x - 4y = 24 +8x +8x -4y = 24 + 8x Geometry CP

  33. Correct! Subtract 6x from both sides!! Great Job! 6x – 12y = -36 6x – 12y = -36 -6x -6x -12y = -36 – 6x Geometry CP

  34. Correct! Add 2x to both sides!! Great Job! -2x – 2y = -14 -2x – 2y = -14 +2x +2x -2y = -14 + 2x Geometry CP

  35. GREAT GAME!!!! Please go back to your seats, we are going to return to our notes and get this first step written down and committed to memory  Geometry CP

  36. First StepExample Problem 1 6x + 3y = 9 Geometry CP

  37. First StepExample Problem 2 -10x + 2y = 8 Geometry CP

  38. First StepExample Problem 3 x - 2y = 4 Geometry CP

  39. First StepExample Problem 4 -x + y = -2 Geometry CP

  40. First StepExample Problem 5 -8x – 2y = -2 Geometry CP

  41. Your Turn • With your shoulder buddy, complete the 10 problems on the next page. • Remember, you are only showing the first step! • You have 5 minutes to get this completed  Geometry CP

  42. Pair Race Directions Equations are going to flash on the screen. The first one to step forward and show the first AND second steps to converting the equation will win. Circle the slope and square on y-intercept What ever side of the room has the most points wins! EVERYONE….Please pay attention  Geometry CP

  43. Example 4x + 2y = 18 The first step is: Subtract 4x from both sides That would look like: 4x + 2y = 18 -4x -4x 2y = 18 – 4x The second step is: Divide everything by 2 2y = 18 – 4x 2 2 2 Final Result: y = 9 – 2x Geometry CP

  44. Example -14x + 7y = 28 The first step is: Add 14x to both sides That would look like: -14x + 7y = 28 +14x +14x 7y = 28 + 14x The second step is: Divide everything by 7 7y = 28 + 14x 7 7 7 Final Result: y = 4 + 2x Geometry CP

  45. Example -8x – 2y = -10 The first step is: Add 8x to both sides That would look like: -8x – 2y = -10 +8x +8x -2y = -10 + 8x The second step is: Divide everything by -2 -2y = -10 + 8x -2 -2 -2 Final Result: y = 5 – 4x Geometry CP

  46. Example 12x – 6y = 18 The first step is: Subtract 12x from both sides That would look like: 12x – 6y = 18 -12x -12x -6y = 18 – 12x The second step is: Divide everything by -6 -6y = 18 – 12x -6 -6 -6 Final Result: y = -3 + 2x Geometry CP

  47. Let’s Race Again! ReadySet GO!! Geometry CP

  48. First Step? Correct! Subtract 4x from both sides!! 4x + 5y = 10 4x + 5y = 10 -4x -4x 5y = 10 – 4x Second Step? Correct! Divide everything by 5!! Geometry CP

  49. 5y = 10 – 4x y = 2 – 4/5x Geometry CP

  50. Correct! Add 6x to both sides!! -6x + 3y = 12 -6x + 3y = 12 +6x +6x 3y = 12 + 6x Second Step? Correct! Divide everything by 3!! Geometry CP

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