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Rewrite the following equation in standard form. $\newline$ $y = 10x + 3$ $\newline$ 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 = 10x + 3

\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 $y = 10x + 3$ . 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 for Isolation: Move the term involving $x$ to the other side of the equation to isolate $y$ . To do this, we subtract $10x$ from both sides of the equation. $y - 10x = 10x + 3 - 10x$ This simplifies to: $y - 10x = 3$
Rearrange for Standard Form: Rearrange the terms to match the standard form. $\newline$ We want the $x$ term to come before the $y$ term, so we write the equation as: $\newline$ $-10x + y = 3$
Ensure Non-Negative Coefficient: Ensure that the coefficient of $x$ is non-negative. $\newline$ Since the standard form requires $A$ to be non-negative, we multiply the entire equation by $-1$ to make the coefficient of $x$ positive. $\newline$ $-1(-10x + y) = -1(3)$ $\newline$ This simplifies to: $\newline$ $10x - y = -3$
Check GCF of Coefficients: Check if the coefficients have a GCF other than $1$ . The coefficients are $10$ , $-1$ , and $-3$ . 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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