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Rewrite the following equation in standard form. $\newline$ $y = x + 2$ $\newline$ 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 = x + 2

\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 Rewrite Standard Form: Start with the given equation. $\newline$ $y = x + 2$ $\newline$ We need to rewrite this equation in the standard form $Ax + By = C$ .
Move Term Left Side: 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. $\newline$ $y - x = x + 2 - x$ $\newline$ This simplifies to: $\newline$ $y - x = 2$
Rearrange Terms Standard Form: Rearrange the terms to match the standard form $Ax + By = C$ . The standard form requires the $x$ term to be first, followed by the $y$ term. $-x + y = 2$
Ensure Positive Coefficient: Ensure that the coefficient of $x$ is positive. $\newline$ In standard form, the coefficient of $x$ is typically positive. If we multiply the entire equation by $-1$ , we will achieve this. $\newline$ $-1(-x + y) = -1(2)$ $\newline$ This simplifies to: $\newline$ $x - y = -2$
Check Coefficients GCF: Check if the coefficients are integers whose greatest common factor (GCF) is $1$ . The coefficients are $1$ , $-1$ , and $-2$ . The GCF of these numbers is indeed $1$ .

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\newline

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