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Rewrite the following equation in standard form. $\newline$ $y = 8x + 1$ $\newline$ 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 + 1

\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 and Standard Form: Identify the given equation and the standard form requirement. $\newline$ The given equation is $y = 8x - 1$ , 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 $1$ .
Move Term to Isolate Variable: Move the term $8x$ to the other side of the equation to isolate the variable $y$ . To do this, we subtract $8x$ from both sides of the equation. $y - 8x = -1$
Rearrange Equation for Standard Form: Rearrange the equation so that the $x$ term comes before the $y$ term. $-8x + y = -1$
Ensure Positive Coefficient: Ensure that the coefficient of $x$ is positive. $\newline$ To do this, we multiply the entire equation by $-1$ to get the standard form. $\newline$ $(-1)(-8x) + (-1)(y) = (-1)(-1)$ $\newline$ $8x - y = 1$

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\newline

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\newline

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\newline

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\newline

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A

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C

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