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Rewrite the following equation in standard form. $\newline$ $y = 4x + 5$ $\newline$ 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 = 4x + 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: Identify the given equation and the standard form requirement. $\newline$ The given equation is $y = 4x - 5$ . 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 Term: Move the term involving $x$ to the other side of the equation to isolate the constant term. $\newline$ To do this, we subtract $4x$ from both sides of the equation. $\newline$ $y - 4x = -5$ $\newline$ However, this is not the standard form yet because the $x$ term should be on the left side of the equation.
Rearrange Terms: Rearrange the terms to place the $x$ term on the left side and the $y$ term on the right side. $\newline$ We write the $x$ term first, followed by the $y$ term, to get the equation in standard form. $\newline$ $-4x + y = -5$
Ensure Positive Coefficient: Ensure that the coefficient of $x$ is positive. $\newline$ Since the standard form requires the coefficient of $x$ to be non-negative, we multiply the entire equation by $-1$ to make the coefficient of $x$ positive. $\newline$ $-1(-4x + y) = -1(-5)$ $\newline$ $4x - y = 5$
Check GCF: Check if the coefficients have a GCF other than $1$ . The coefficients are $4$ , $-1$ , and $5$ . The GCF of these numbers is $1$ , so we do not need to divide the entire equation by any number to reduce the coefficients.

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