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Rewrite the following equation in standard form. $\newline$ $y = 3x + 4$ $\newline$ 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 $1$ . $\newline$ _____

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Write linear equations in standard form

Full solution

Q. Rewrite the following equation in standard form.

\newline

y = 3x + 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

.

\newline

_____

Identify Equation & Requirement: Identify the given equation and the standard form requirement. $\newline$ The given equation is $y = 3x + 4$ . 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 to Isolate Constant: 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. $\newline$ $y - 3x = 3x + 4 - 3x$ $\newline$ This simplifies to: $\newline$ $y - 3x = 4$
Rearrange Terms to Standard Form: 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. $-3x + y = 4$
Ensure Non-Negative Coefficient: Ensure that the coefficient of $x$ is non-negative. $\newline$ If the coefficient of $x$ is negative, we can multiply the entire equation by $-1$ to make it positive. However, in this case, it is not necessary because we can simply reorder the terms without changing their signs. $\newline$ So, we rewrite the equation as: $\newline$ $3x - y = -4$
Check for GCF: Check if the coefficients have a GCF other than $1$ . The coefficients are $3$ , $-1$ , and $-4$ . The GCF of these numbers is $1$ , so we do not need to divide the entire equation by any number to reduce the coefficients.

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