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Rewrite the following equation in standard form. $\newline$ $y = 10x + 8$ $\newline$ 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 + 8

\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 Given Equation: Identify the given equation and the desired form. $\newline$ The given equation is $y = 10x + 8$ , and we want to rewrite it in the standard form $Ax + By = C$ .
Move Term Involving $x$ : Move the term involving $x$ to the other side of the equation. $\newline$ To do this, we subtract $10x$ from both sides of the equation. $\newline$ $y - 10x = 10x + 8 - 10x$ $\newline$ This simplifies to $y - 10x = 8$ .
Rearrange Terms to Match: Rearrange the terms to match the standard form. $\newline$ The standard form is $Ax + By = C$ , so we need to write the $x$ term first. $\newline$ $-10x + y = 8$
Check Coefficients for GCF: Check if the coefficients are integers and their greatest common factor (GCF) is $1$ . The coefficients are $-10$ , $1$ , and $8$ . The GCF of these numbers is $1$ .
Ensure Positive Coefficient: Ensure that the coefficient of $x$ is positive. $\newline$ If the coefficient of $x$ is negative, we can multiply the entire equation by $-1$ to make it positive. $\newline$ Multiplying by $-1$ , we get: $\newline$ $10x - y = -8$

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