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Rewrite the following equation in standard form. $\newline$ $y = 8x + 6$ $\newline$ 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 = 8x + 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 Standard Form: Identify the given equation and the standard form requirement. $\newline$ The given equation is $y = 8x + 6$ . 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 Isolation: Move the term involving $x$ to the other side of the equation to isolate the constant term on one side. $\newline$ To do this, we subtract $8x$ from both sides of the equation: $\newline$ $y - 8x = 8x + 6 - 8x$ $\newline$ This simplifies to: $\newline$ $-y + 8x = 6$
Multiply by $-1$ : Multiply the entire equation by $-1$ to make the coefficient of $x$ positive, as is customary in standard form. $\newline$ $-1(-y + 8x) = -1(6)$ $\newline$ This simplifies to: $\newline$ $y - 8x = -6$
Rearrange for Standard Form: Rearrange the terms to match the standard form $Ax + By = C$ . $8x - y = 6$

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