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

\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 $y = 6x - 3$ , 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 Term to Isolate $y$ : Move the term involving $x$ to the other side of the equation to isolate $y$ . To do this, we subtract $6x$ from both sides of the equation. $y - 6x = -3$ However, this is not the standard form yet because the $x$ term should be before the $y$ term.
Rearrange for Standard Form: Rearrange the terms to match the standard form $Ax + By = C$ . We want the $x$ term first, so we write the equation as: $-6x + y = -3$
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. $\newline$ Multiplying by $-1$ , we get: $\newline$ $6x - y = 3$ $\newline$ Now the equation is in standard form with $A = 6$ , $B = -1$ , and $C = 3$ .

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