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Rewrite the following equation in standard form. $\newline$ $y = 8x + 5$ $\newline$ 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 = 8x + 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 & Standard Form: Identify the given equation and the standard form requirement. $\newline$ The given equation is $y = 8x + 5$ , 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 x-term to Left: Move the term $8x$ from the right side of the equation to the left side to get the x-term and the y-term on the same side. $\newline$ To do this, we subtract $8x$ from both sides of the equation: $\newline$ $y - 8x = 8x + 5 - 8x$ $\newline$ This simplifies to: $\newline$ $-y + 8x = 5$
Multiply by $-1$ : Multiply the entire equation by $-1$ to make the coefficient of $x$ positive, as is customary in standard form. $\newline$ $-1(-y + 8x) = -1(5)$ $\newline$ This simplifies to: $\newline$ $y - 8x = -5$
Rearrange for Standard Form: Rearrange the terms to match the standard form $Ax + By = C$ . We want the $x$ -term first, followed by the $y$ -term, so we write: $-8x + y = -5$
Check Coefficients for GCF: Check if the coefficients have a GCF other than $1$ . The coefficients are $-8$ , $1$ , and $-5$ . The GCF of these numbers is $1$ .
Make Coefficient of $x$ Positive: Since the GCF is $1$ and the coefficient of $x$ is negative, we multiply the entire equation by $-1$ to make the coefficient of $x$ positive. $\newline$ $-1(-8x + y) = -1(-5)$ $\newline$ This simplifies to: $\newline$ $8x - y = 5$

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