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Rewrite the following equation in standard form. $\newline$ $y = 4x + 10$ $\newline$ 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 $1$ . $\newline$ _____

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Write linear equations in standard form

Full solution

Q. Rewrite the following equation in standard form.

\newline

y = 4x + 10

\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

.

\newline

_____

Given Equation: Start with the given equation. $\newline$ $y = 4x + 10$ $\newline$ We need to rearrange this equation into the standard form, which is $Ax + By = C$ .
Rearrange Equation: Move the term $4x$ to the left side of the equation by subtracting $4x$ from both sides. $\newline$ $y - 4x = 4x + 10 - 4x$ $\newline$ This simplifies to: $\newline$ $-4x + y = 10$
Make Coefficient Positive: The standard form of a linear equation should have the $x$ -term first, followed by the $y$ -term, and then the constant. However, the coefficient of $x$ should be positive. Multiply the entire equation by $-1$ to make the coefficient of $x$ positive. $\newline$ $-1(-4x + y) = -1(10)$ $\newline$ This simplifies to: $\newline$ $4x - y = -10$
Check Coefficients: Check that the coefficients are integers and that their greatest common factor (GCF) is $1$ . The coefficients are $4$ , $-1$ , and $-10$ . The GCF of these numbers is $1$ .

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