To write an equation in standard form, it typically refers to rewriting it as a linear equation in the form:

Ax + By = C

Where:

• $A, B,$ and $C$ are integers.
• $A$ is non-negative ($A \geq 0$).
• $A, B,$ and $C$ are often simplified so there are no fractions or decimals.

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Steps to Convert to Standard Form:

1. Eliminate fractions or decimals: Multiply through by the least common denominator (LCD) to clear any fractions or decimals.

2. Rearrange terms: Move all terms involving variables ($x$ and $y$) to the left side of the equation, leaving the constant $C$ on the right.

3. Simplify coefficients: Make sure $A$, $B$, and $C$ are integers. If $A$ is negative, multiply the entire equation by $-1$ to make it positive.

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Example:

Convert $y = \frac{2}{3}x - 4$ to standard form.

1. Eliminate fractions: Multiply through by 3 (the denominator): $3y = 2x - 12$

2. Rearrange terms: Move $2x$ to the left side: $-2x + 3y = -12$

3. Simplify coefficients: Multiply by $-1$ to make $A$ positive: $2x - 3y = 12$

Standard form: $2x - 3y = 12$.

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Let me know if you’d like detailed steps for another example or additional help!

Expanding Ideas:

1. How do you identify $A, B,$ and $C$ when rearranging an equation?
2. Why is it important to clear fractions and decimals in standard form?
3. How does the process differ for nonlinear equations?
4. What happens if $A, B,$ or $C$ are not integers?
5. How do you convert quadratic equations into their respective standard forms?

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Tip: Always verify your standard form by substituting a point from the original equation to ensure equivalence.