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Rewrite the following equation in standard form. $\newline$ $y = 6x + 5$ $\newline$ 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 + 5

\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 Operation Isolate: Start with the given equation. $\newline$ $y = 6x - 5$ $\newline$ Which operation should be used to isolate the constant, $-5$ ? $\newline$ In $y = 6x - 5$ , $6x$ is positive. $\newline$ Subtraction is used to isolate $-5$ .
Rewrite Equation Standard Form: Rewrite the equation in standard form. $\newline$ $y = 6x - 5$ $\newline$ Subtract $6x$ from both sides to move the x-term to the left side of the equation. $\newline$ $y - 6x = -5$
Rearrange Terms Match Standard Form: Rearrange the terms to match the standard form $Ax + By = C$ .
$-6x + y = -5$
However, it is customary to write the $x$ -term first and to have the coefficient of $x$ be positive in standard form.
Multiply the entire equation by $-1$ to make the coefficient of $x$ positive.
$-1(-6x + y) = -1(-5)$
$6x - y = 5$

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