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Rewrite the following equation in standard form. $\newline$ $y = 5x + 8$ $\newline$ 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 = 5x + 8

\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

_____

Identify Equation & Standard Form: Identify the given equation and the standard form requirement. $\newline$ The given equation is $y = 5x + 8$ . 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.
Rearrange Equation: Rearrange the equation to get terms involving $x$ and $y$ on one side and the constant on the other side. $\newline$ To do this, we will subtract $5x$ from both sides of the equation to move the $x$ term to the left side. $\newline$ $y - 5x = 5x + 8 - 5x$ $\newline$ This simplifies to: $\newline$ $-5x + y = 8$
Ensure Non-Negative Coefficient: Ensure that the coefficient of $x$ is non-negative. $\newline$ The standard form prefers the coefficient of $x$ to be positive. To achieve this, we can multiply the entire equation by $-1$ . $\newline$ $-1(-5x + y) = -1(8)$ $\newline$ This simplifies to: $\newline$ $5x - y = -8$
Check GCF of Coefficients: Check if the coefficients have a GCF other than $1$ . The coefficients of the equation $5x - y = -8$ are $5$ , $-1$ , and $-8$ . The GCF of these numbers is $1$ .
Write Final Equation: Write the final equation in standard form. $\newline$ The equation is now in standard form with $A = 5$ , $B = -1$ , and $C = -8$ . $\newline$ The final standard form of the equation is: $\newline$ $5x - y = -8$

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\newline

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