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Rewrite the following equation in standard form. $\newline$ $y = 10x + 1$ $\newline$ 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 = 10x + 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

.

Given Equation: Start with the given equation. $\newline$ $y = 10x + 1$ $\newline$ We need to rearrange this equation into the standard form, which is $Ax + By = C$ .
Rearrange Equation: Move the term involving $x$ to the other side of the equation by subtracting $10x$ from both sides. $\newline$ $y - 10x = 10x + 1 - 10x$ $\newline$ This simplifies to: $\newline$ $-10x + y = 1$
Move x Term: The standard form of a linear equation should have the $x$ -term first, and the coefficient of $x$ should be positive. Multiply the entire equation by $-1$ to achieve this. $\newline$ $-1(-10x + y) = -1(1)$ $\newline$ This simplifies to: $\newline$ $10x - y = -1$
Multiply by $-1$ : To make sure the equation is in standard form, we need to check if the coefficients are integers whose greatest common factor (GCF) is $1$ . The coefficients are $10$ , $-1$ , and $-1$ . Their GCF is indeed $1$ .

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