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Rewrite the following equation in standard form. $\newline$ $y = 3x + 9$ $\newline$ 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 + 9

\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 and Form: Identify the given equation and the desired form. $\newline$ The given equation is $y = 3x + 9$ , and we want to rewrite it in the standard form $Ax + By = C$ .
Move Term Involving $x$ : Move the term involving $x$ to the other side of the equation. $\newline$ To do this, we subtract $3x$ from both sides of the equation to get $-3x + y = 9$ .
Check Coefficients and GCF: Check if the coefficients are integers and their greatest common factor (GCF) is $1$ . $\newline$ The coefficients in the equation $-3x + y = 9$ are $-3$ , $1$ , and $9$ . The GCF of these numbers is $1$ .
Write Final Equation: Write the final equation in standard form. $\newline$ The equation $-3x + y = 9$ is already in standard form, with $A = -3$ , $B = 1$ , and $C = 9$ .

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