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Rewrite the following equation in standard form. $\newline$ $y = 7x + 5$ $\newline$ 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 = 7x + 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

.

Identify Equation Requirement: Identify the given equation and the standard form requirement. $\newline$ The given equation is $y = 7x + 5$ , 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 Left: Move the term involving $x$ to the left side of the equation. $\newline$ To do this, we subtract $7x$ from both sides of the equation to get $-7x + y = 5$ .
Check Coefficient GCF: Check if the coefficients have a GCF other than $1$ . The coefficients of the terms $-7x$ and $y$ are $-7$ and $1$ , respectively. Their GCF is $1$ , so we do not need to divide the entire equation by any number to reduce the coefficients.
Ensure Non-Negative Coefficient: Ensure that the coefficient of $x$ is non-negative. $\newline$ Since the standard form requires $A$ to be non-negative, we multiply the entire equation by $-1$ to get $7x - y = -5$ .

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