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

\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 and Requirement: Identify the given equation and the standard form requirement. $\newline$ The given equation is $y = x + 6$ , 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 $x$ Term Left: Move the $x$ term to the left side of the equation. $\newline$ To do this, we subtract $x$ from both sides of the equation to get $-x + y = 6$ .
Multiply by $-1$ : Multiply the entire equation by $-1$ to make the coefficient of $x$ positive. $\newline$ Multiplying by $-1$ , we get $x - y = -6$ . This is now in the standard form, with $A = 1$ , $B = -1$ , and $C = -6$ .
Check Coefficients GCF: Check if the coefficients have a GCF other than $1$ . The coefficients are $1$ , $-1$ , and $-6$ . The GCF of these numbers is $1$ .

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