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Starter: Equations of lines What are the equations of the following lines?

y. 5. 4. 3. 2. 1. x. -5. -4. -3. -2. -1. 0. 1. 2. 3. 4. 5. -1. -2. -3. -4. -5. Starter: Equations of lines What are the equations of the following lines?. B. A. C. D. E. y. 5. 4. 3. 2. 1. x. -5. -4. -3. -2. -1. 0. 1. 2. 3. 4. 5. -1. -2. -3. -4. -5.

norman-bowman
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Starter: Equations of lines What are the equations of the following lines?

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  1. y 5 4 3 2 1 x -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 Starter: Equations of linesWhat are the equations of the following lines? B A C D E

  2. y 5 4 3 2 1 x -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 Starter: Equations of linesWhat are the equations of the following lines? B A A: y = x C D E

  3. y 5 4 3 2 1 x -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 Starter: Equations of linesWhat are the equations of the following lines? B A A: y = x B: y = x + 4 C D E

  4. y 5 4 3 2 1 x -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 Starter: Equations of linesWhat are the equations of the following lines? B A A: y = x B: y = x + 4 C: y = x - 2 C D E

  5. y 5 4 3 2 1 x -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 Starter: Equations of linesWhat are the equations of the following lines? B A A: y = x B: y = x + 4 C: y = x – 2 D: y = -x + 1 C D E

  6. y 5 4 3 2 1 x -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 Starter: Equations of linesWhat are the equations of the following lines? B A A: y = x B: y = x + 4 C: y = x – 2 D: y = -x + 1 E: y = -x - 4 C D E

  7. y 5 4 3 2 1 x -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 Objective: To understand simultaneous equations Where do the lines C and E cross? C E

  8. y 5 4 3 2 1 x -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 Objective: To understand simultaneous equations Where do the lines C and E cross? By observation they cross at (-1, -3) C E

  9. y 5 4 3 2 1 x -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 Objective: To understand simultaneous equations Where do the lines C and E cross? By observation they cross at (-1, -3) You could have worked this out algebraically without drawing the graphs……… C E

  10. y 5 4 3 2 1 x -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 Objective: To understand simultaneous equations The equations of the lines are y = x – 2 …and… y = -x – 4 C E

  11. y 5 4 3 2 1 x -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 Objective: To understand simultaneous equations The equations of the lines are y = x – 2 …and… y = -x – 4 Because they are both y = something, we can write x – 2 = -x - 4 C E

  12. y 5 4 3 2 1 x -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 Objective: To understand simultaneous equations The equations of the lines are y = x – 2 …and… y = -x – 4 Because they are both y = something, we can write x – 2 = -x – 4 2x = -2 C E

  13. y 5 4 3 2 1 x -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 Objective: To understand simultaneous equations The equations of the lines are y = x – 2 …and… y = -x – 4 Because they are both y = something, we can write x – 2 = -x – 4 2x = -2 x = -1 C E

  14. y 5 4 3 2 1 x -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 Objective: To understand simultaneous equations The equations of the lines are y = x – 2 …and… y = -x – 4 Because they are both y = something, we can write x – 2 = -x – 4 2x = -2 x = -1 Therefore y = -1 – 2 = -3 They cross at (-1, -3) C E

  15. Objective: To understand simultaneous equations Simultaneous equations are written in the form: y – 3x = 2 y – 2x = 5

  16. Objective: To understand simultaneous equations Simultaneous equations are written in the form: y – 3x = 2 y – 2x = 5 This is the same as: y = 3x + 2 y = 2x + 5

  17. Objective: To understand simultaneous equations Simultaneous equations are written in the form: y – 3x = 2 y – 2x = 5 This is the same as: y = 3x + 2 y = 2x + 5 So, 3x + 2 = 2x + 5

  18. Objective: To understand simultaneous equations Simultaneous equations are written in the form: y – 3x = 2 y – 2x = 5 This is the same as: y = 3x + 2 y = 2x + 5 So, 3x + 2 = 2x + 5 x = 3 If x = 3, y = 11

  19. Objective: To understand simultaneous equations Questions: Solve the simultaneous equations 1.) y – 4x = 1 5.) 2x – y = 4 y – x = 7 -x – y = 7 2.) x + y = 8 6.) 2x – y = 6 x + 2y = 14 x – y = 2 3.) y + x = 6 7.) 3x + 2y = 18 y + 2x = 10 3x + 4y = 24 Extension/plenary 4.) 3x + y = 10 8.) 2x + 3y = 24 4x + y = 13 x + 2y = 14

  20. Extension 2x + 3y = 24 x + 2y = 14 x = 14 – 2y

  21. Extension 2x + 3y = 24 x + 2y = 14 x = 14 – 2y 2(14 – 2y) + 3y = 24

  22. Extension 2x + 3y = 24 x + 2y = 14 x = 14 – 2y 2(14 – 2y) + 3y = 24 28 – 4y + 3y = 24

  23. Extension 2x + 3y = 24 x + 2y = 14 x = 14 – 2y 2(14 – 2y) + 3y = 24 28 – 4y + 3y = 24 -y = -4

  24. Extension 2x + 3y = 24 x + 2y = 14 x = 14 – 2y 2(14 – 2y) + 3y = 24 28 – 4y + 3y = 24 -y = -4 y = 4 x = 14 – (2 X 4)

  25. Extension 2x + 3y = 24 x + 2y = 14 x = 14 – 2y 2(14 – 2y) + 3y = 24 28 – 4y + 3y = 24 -y = -4 y = 4 x = 14 – (2 X 4) x = 14 - 8

  26. Extension 2x + 3y = 24 x + 2y = 14 x = 14 – 2y 2(14 – 2y) + 3y = 24 28 – 4y + 3y = 24 -y = -4 y = 4 x = 14 – (2 X 4) x = 14 – 8 x = 6

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