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Rewrite the following equation in standard form. $\newline$ $y = 6x + 4$ $\newline$ 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 $1$ .

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Write linear equations in standard form

Full solution

Q. Rewrite the following equation in standard form.

\newline

y = 6x + 4

\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

.

Identify Equation & Standard Form: Identify the given equation and the standard form requirement. $\newline$ The given equation is $y = 6x - 4$ , and 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 term. $\newline$ To do this, we subtract $6x$ from both sides of the equation. $\newline$ $y - 6x = -4$
Rearrange Terms to Match: Rearrange the terms to match the standard form $Ax + By = C$ . We want the $x$ term to come before the $y$ term, so we write the equation as: $-6x + y = -4$
Ensure Non-Negative Coefficient: Ensure that the coefficient of $x$ is non-negative. $\newline$ Since the standard form requires $A$ to be non-negative, we multiply the entire equation by $-1$ to make the coefficient of $x$ positive. $\newline$ $6x - y = 4$
Check Coefficients for GCF: Check that the coefficients are integers with a GCF of $1$ . The coefficients are $6$ , $-1$ , and $4$ . The GCF of these numbers is $1$ , so they meet the requirement.

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