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Rewrite the following equation in standard form. $\newline$ $y = 10x + 2$ $\newline$ 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 + 2

\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 rearrangement: To convert the equation to standard form, we need to rearrange it so that it fits the format $Ax + By = C$ . We start with the given equation: $\newline$ $y = 10x + 2$
Subtracting $10$ x: We want to move the term involving x to the other side of the equation. To do this, we subtract $10x$ from both sides of the equation: $\newline$ $y - 10x = 10x + 2 - 10x$
Simplifying the equation: Simplifying the equation by canceling out the $10x$ on the right side gives us: $y - 10x = 2$
Switching sides: The standard form of a linear equation is $Ax + By = C$ , where $A$ is a positive integer. Since we have $-10x$ , we will rewrite the equation by switching the sides to make the coefficient of $x$ positive: $\newline$ $10x - y = -2$
Multiplying by $-1$ : However, we want the equation in the form $Ax + By = C$ , so we multiply the entire equation by $-1$ to get the terms in the correct order and to ensure that $A$ is positive: $\newline$ $-1(10x - y) = -1(-2)$
Final standard form: Multiplying each term by $-1$ gives us the final standard form of the equation: $-10x + y = 2$

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