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Rewrite the following equation in standard form. $\newline$ $y = x + 7$ $\newline$ 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 $1$ . $\newline$ _____

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Write linear equations in standard form

Full solution

Q. Rewrite the following equation in standard form.

\newline

y = x + 7

\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

.

\newline

_____

Rewrite in Standard Form: Start with the given equation. $\newline$ $y = x + 7$ $\newline$ We need to rewrite this equation in the standard form $Ax + By = C$ .
Move x Term Left: Move the term with $x$ to the left side of the equation. $\newline$ To do this, we subtract $x$ from both sides of the equation. $\newline$ $y - x = x + 7 - x$ $\newline$ This simplifies to: $\newline$ $y - x = 7$
Rearrange Terms: Rearrange the terms to match the standard form $Ax + By = C$ . We want the $x$ term first, followed by the $y$ term. $-x + y = 7$
Multiply by $-1$ : Multiply the entire equation by $-1$ to make the coefficient of $x$ positive. $\newline$ $-1(-x + y) = -1(7)$ $\newline$ This simplifies to: $\newline$ $x - y = -7$
Check Coefficients: Check that the coefficients are integers and their greatest common factor (GCF) is $1$ . The coefficients are $1$ , $-1$ , and $-7$ . The GCF of $1$ and $-1$ is $1$ .

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