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Rewrite the following equation in standard form. $\newline$ $y = 4x + 1$ $\newline$ 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 = 4x + 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 & Requirement: Identify the given equation and the standard form requirement. $\newline$ The given equation is $y = 4x + 1$ , 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 $1$ , 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 $4x$ from both sides of the equation to move the term involving $x$ to the left side. $\newline$ $y - 4x = 1$ $\newline$ However, the standard form requires the $x$ term to be before the $y$ term, so we rewrite it as: $\newline$ $-4x + y = 1$
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. If it is negative, we can multiply the entire equation by $-1$ to make it positive. $\newline$ Multiplying by $-1$ , we get: $\newline$ $4x - y = -1$
Check Coefficients & GCF: Check if the coefficients are integers with a GCF of $1$ . The coefficients $4$ , $-1$ , and the constant $-1$ are integers, and their GCF is $1$ .

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