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Rewrite the following equation in standard form. $\newline$ $y = 3x + 5$ $\newline$ 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 = 3x + 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

.

Rearrange equation: To convert the equation $y = 3x + 5$ into standard form, we need to rearrange the terms so that the $x$ and $y$ terms are on one side of the equation and the constant is on the other side. We want it in the form $Ax + By = C$ .
Subtract $3x$ : Subtract $3x$ from both sides of the equation to move the $x$ term to the left side. This gives us $-3x + y = 5$ .
Check coefficients: Check if the coefficients $A$ , $B$ , and $C$ are integers whose greatest common factor (GCF) is $1$ . In this case, the coefficients are $-3$ , $1$ , and $5$ , which do not have a common factor other than $1$ .
Equation in standard form: The equation $-3x + y = 5$ is now in standard form, with $A = -3$ , $B = 1$ , and $C = 5$ . This satisfies the conditions for standard form, where $A$ and $B$ are not both zero, and $A$ , $B$ , and $C$ are integers with a GCF of $1$ .

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