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Rewrite the following equation in standard form. $\newline$ $y = 3x + 6$ $\newline$ 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 = 3x + 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

.

Given Equation: Start with the given equation. $\newline$ $y = 3x - 6$ $\newline$ We need to rearrange this equation into the standard form, which is $Ax + By = C$ .
Move $x$ Term: Move the term with $x$ to the other side of the equation by subtracting $3x$ from both sides. $\newline$ $y - 3x = -6$ $\newline$ This is not yet in standard form because the $x$ term should be before the $y$ term.
Rearrange Terms: Rearrange the terms to place the $x$ term first. $-3x + y = -6$
Make Coefficient Positive: The standard form of a linear equation should have a positive coefficient for $x$ . Multiply the entire equation by $-1$ to make the coefficient of $x$ positive. $\newline$ $-1(-3x + y) = -1(-6)$ $\newline$ $3x - y = 6$
Check Coefficients: Check that the coefficients are integers and their greatest common factor (GCF) is $1$ . The coefficients are $3$ , $-1$ , and $6$ . The GCF of these numbers is $1$ .

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