Standard Form for Linear Equations



Algebra 1

Unit 4.5 Standard Form Part 2

STANDARD FORM: Ax + By = C

• Rules for Standard Form:

1. x and y terms should be together on left side of equal sign, in alphabetical order.

2. Constant (term w/o variable) should be on right side of equal sign.

3. # in front of “x” must be positive.

4. No fractions!

5. Greatest Common Factor should be 1!

• Steps to write an equation in Standard Form:

1. Clear all fractions by multiplying every term by a least common multiple of the denominators.

2. Move the “x” and “y” terms to the left side of the equal sign. Change the sign of

any term moved from one side of the equal sign to the other.

3. Move the constants (terms with no variable) to the right side of the equal sign.

Change the sign of any term moved. Combine like terms.

4. If “x” is negative, change the sign of every term in the equation. This will make

the “x” positive.

5. Simplify the equation by dividing by the greatest common factor of every term.

EXAMPLES:

Write each equation in Standard Form.

1. y = -4x – 6 2. 4y + 3 = -x – 2 3. -x + y = 4 4. y + 2 = 3(x – 5)

5. [pic] 6. [pic] 7. [pic]

Algebra 1 Name_______________________

4.5 Period 1 2 3 4 5 6 7

ASSIGNMENT

|Write each equation in Standard Form. C Level |

|1. [pic] |2. [pic] |3. [pic] |

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|4. [pic] |5. [pic] |6. 5y + 3x = -1 |

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|7. -x – 2y = 1 |8. -7x + y = -2 |9. -4x – 4y = 8 |

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| B Level |

|10. y = 7x - 2 |11. [pic] |12. y = 4(x + 3) |

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|13. [pic] |14. [pic] |15. -2x + 8 = y - 3 |

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|16. y + 7 = -5(x + 3) |17. y – 6 = -2(x – 7) |18. y – 10 = 4(x + 6) |

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| A Level |

|19. [pic] |20. [pic] |21. [pic] |

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|22. [pic] |23. [pic] |24. [pic] |

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PRACTICE TEST

|Level C |Level B |Level A |

|1C. Write the following equation in Standard Form.|1B. Write the following equation in Standard Form.|1A. Write the following equation in Standard Form.|

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|[pic] |[pic] |[pic] |

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RANDOM ANSWERS

|x + 2y = -4 |2x – 4y = -3 |x + y = 5 |x + 4y = 3 |

|2x + y = 3 |x + 2y = -1 |3x + 5y = -1 |7x – y = 2 |

|2x + 3y = 3 |7x – y = 2 |2x + y = 11 |2x – y = 3 |

|3x + y = -4 |x + 4y = 5 |3x – y = 3 |5x + y = -22 |

|4x – y = -12 |4x – y = -34 |x + 2y = -10 |x + y = -2 |

|6x – 2y = -3 |2x + y = 20 |2x – 3y = 6 |7x – 8y = 37 |

|Practice Test |1C 3x – y = 5 |1B 8x – y = 3 |1A 2x – 3y = -18 |

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