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Rewrite the following equation in standard form. $\newline$ $y = 3x + 8$ $\newline$ Hint: The standard form of a linear equation is $Ax + By = C$ where $A$ and $B$ are not both zero, and $A$ , $B$ , and $C$ are integers whose GCF is $1$ . $\newline$ _____

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Write linear equations in standard form

Full solution

Q. Rewrite the following equation in standard form.

\newline

y = 3x + 8

\newline

Hint: The standard form of a linear equation is

Ax + By = C

where

A

and

B

are not both zero, and

A

,

B

, and

C

are integers whose GCF is

1

.

\newline

_____

Identify Equation & Requirement: Identify the given equation and the standard form requirement. $\newline$ The given equation is $y = 3x + 8$ . We need to rewrite it in the standard form $Ax + By = C$ , where $A$ , $B$ , and $C$ are integers with a greatest common factor (GCF) of $1$ , and $A$ should be non-negative.
Move Term Involving $x$ : Move the term involving $x$ to the other side of the equation to isolate the constant on one side. $\newline$ To do this, we subtract $3x$ from both sides of the equation: $\newline$ $y - 3x = 3x + 8 - 3x$ $\newline$ This simplifies to: $\newline$ $y - 3x = 8$
Rearrange Terms to Match: Rearrange the terms to match the standard form $Ax + By = C$ . We want the $x$ term first, followed by the $y$ term, equaling the constant: $-3x + y = 8$
Ensure Non-Negative Coefficient: Ensure that the coefficient of $x$ is non-negative. $\newline$ If we multiply the entire equation by $-1$ , we get: $\newline$ $3x - y = -8$ $\newline$ However, since the coefficient of $x$ in the original rearrangement $(-3x + y = 8)$ is negative, we do not need to multiply by $-1$ because the standard form does not require $A$ to be positive, only non-negative. Therefore, we can leave the equation as $-3x + y = 8$ .

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