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Rewrite the following equation in standard form. $\newline$ $y = 5x + 1$ $\newline$ 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 = 5x + 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

.

Subtracting to isolate x-term: The equation given is $y = 5x - 1$ . To rewrite it in standard form, we need to get the terms involving variables on one side and the constant on the other side. We can do this by subtracting $5x$ from both sides of the equation. $\newline$ Calculation: $y - 5x = -1$
Rearranging terms: Now we have $y - 5x = -1$ , but the standard form requires the $x$ -term to come before the $y$ -term. So, we rearrange the terms to get the $x$ -term first. $\newline$ Calculation: $-5x + y = -1$
Making $x$ -term positive: The standard form of a linear equation is $Ax + By = C$ , where $A$ is a positive integer. Since $-5$ is negative, we multiply the entire equation by $-1$ to make the coefficient of $x$ positive. $\newline$ Calculation: $(-1)(-5x) + (-1)(y) = (-1)(-1)$
Final standard form: After multiplying by $-1$ , we get the equation in standard form. $\newline$ Calculation: $5x - y = 1$

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