Standard Form for Linear Equations



Algebra 1

Unit 4.4 Standard Form Part 1

There are 2 main formats for writing an equation:

Slope-Intercept Form: y = mx + b y = -3x + 2

Standard Form: Ax + By = C 6x + 2y = 4

This lesson focuses on STANDARD FORM! Ax + By = C … 6x + 2y = 4

• Rules for Standard Form:

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

6x + 2y = 4

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

6x + 2y = 4

3. # in front of “x” must be positive

6x + 2y = 4

4. No fractions!

6x + 2y = 4

Examples:

1. Which of the following equations is written in standard form. (circle the answer)

a. -2x + y = 7 b. y = 2x + 7 c. 2x – y = -7

2. Which of the following equations is written in standard form. (circle the answer)

a. [pic] b. [pic] c. x - 8y = -4

Which of the rules for Standard form is the following equation not following? Write every rule not being followed.

a. [pic] b. [pic] c. [pic]

1. Which of the following equations is written in standard form. (circle the answer)

a. -2x + y = 7 b. y = 2x + 7 c. 2x – y = -7

2. Which of the following equations is written in standard form. (circle the answer)

a. [pic] b. [pic] c. x - 8y = -4

1. Which of the following equations is written in standard form. (circle the answer)

a. -2x + y = 7 b. y = 2x + 7 c. 2x – y = -7

2. Which of the following equations is written in standard form. (circle the answer)

a. [pic] b. [pic] c. x - 8y = -4

1. Which of the following equations is written in standard form. (circle the answer)

a. -2x + y = 7 b. y = 2x + 7 c. 2x – y = -7

2. Which of the following equations is written in standard form. (circle the answer)

a. [pic] b. [pic] c. x - 8y = -4

1. Which of the following equations is written in standard form. (circle the answer)

a. -2x + y = 7 b. y = 2x + 7 c. 2x – y = -7

2. Which of the following equations is written in standard form. (circle the answer)

a. [pic] b. [pic] c. x - 8y = -4

Algebra 1 Name_______________________

4.4 Period 1 2 3 4 5 6 7

ASSIGNMENT

|Write the 4 rules for writing and equation in Standard Form, in any order. |

|Then give an example of an equation not following the given rule.      C Level |

|RULE |EXAMPLE |

|1. | |

|2. | |

|3. | |

|4. | |

|Which of the following equations is written in standard form? (circle the answer)      B Level |

|5. |6. |7. |

|a. -2x + 3y = 6 |a. [pic] |a. x + 9 = -3y |

| | | |

|b.   2x - 3y = -6 |b.   3x + 4y - 3 = -7 |b.   -x - 3y = 9 |

| | | |

|c.    [pic] |c.    -3x - 4y = 4 |c.    x + 3y = -9 |

| | | |

|d.   -2x – 6 = -3y |d.   3x + 4y = -4 |d.    [pic] |

|Which of the following equations is not written in standard form? (circle the answer)       |

|8. |9. |10. |

|a. 5x + 3y = 7 |a. 3x + 4y = -4 |a. x + 3y – 4 = 6 |

| | | |

|b.   9x – y = -1 |b.   5x + 2y = 9 |b.   x + y = 2 |

| | | |

|c.    –x + y = 7 |c.    6x - y = 3 |c.    10x – y = -3 |

| | | |

|d.   2x + 4y = -2 |d.   [pic] |d.    9x + 7y = 9 |

| | | |

| | | |

| | | |

| | | |

| | | |

|Which of the rules for Standard form is the following equation not following?                A Level |

|Write every rule not being followed. |

|11. 6y + 3x = 4 |12. -3x – 4y = 6 |13. -x + y -3 = -5 |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

|14. [pic] |15. y = 3x - 7 |16. [pic] |

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PRACTICE TEST

|Level C |Level B |Level A |

|1C. Write the 4 rules for Standard Form in any |1B. Which of the following equations is correctly |1A. Which of the rules for Standard form is the |

|order. |written in Standard Form? |following equation not following? Write every rule |

| | |not being followed. |

|1. |½x - y = -3 | |

| | |[pic] |

|2. |-x + 5y = -6 | |

| | | |

|3. |3x – 4y = -7 | |

| | | |

|4. |y = 6x - 3 | |

| | | |

ANSWER KEY

|Order of Answers can vary for 1-4 |Examples of rule not |

| |being followed. (will vary) |

|1. x and y terms should be together on left side of equal sign, in in alphabetical order. | 4y + 3x = 7 |

|2. Constant (term w/o variable) should be on right side of equal | 6x – 3y – 4 = 10 |

|sign. | |

|3. # in front of “x” must be positive | -4x + y = 6 |

|4. No fractions! |  [pic] |

|5. b |6. d |7. c |

|8. c |9. d |10. a |

|11. x and y terms should be |12. x-term should be |13. -x-term should be |

|alphabetical order |           positive |positive |

| | |-constant on right |

|14. No fractions |15. x and y terms on left |16. -No fractions |

| | |-constants on right |

| | |-x and y term on left |

|PRACTICE TEST | | |

|1C 1. x and y terms on left |1B c |1A -No fractions |

|and in alpha order | |-x-term should be |

|2. x-term is positive | |  positive |

|3. constants on right | | |

|4. No fractions! | | |

-----------------------

x and y terms

Constant

x-term is positive

NO terms have fractions

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