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Rewrite the following equation in standard form. $\newline$ $y = 4x + 8$ $\newline$ 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 $1$ .

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Write linear equations in standard form

Full solution

Q. Rewrite the following equation in standard form.

\newline

y = 4x + 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

.

Start Equation Rearrangement: Start with the given equation. $\newline$ $y = 4x - 8$ $\newline$ We need to rearrange this equation to 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 $4x$ from both sides. $\newline$ $y - 4x = -8$ $\newline$ This is not the standard form yet because the standard form requires the $x$ term to be before the $y$ term.
Rearrange Terms: Rearrange the terms to place the $x$ term before the $y$ term. $\newline$ $-4x + y = -8$ $\newline$ Now the equation is in the form of $Ax + By = C$ , but we need to ensure that $A$ is a positive integer.
Make A Positive: Multiply the entire equation by $-1$ to make $A$ positive. $\newline$ $-1(-4x + y) = -1(-8)$ $\newline$ $4x - y = 8$ $\newline$ Now the equation is in standard form with $A$ , $B$ , and $C$ as integers, and $A$ is positive.

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