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

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Write linear equations in standard form

Full solution

Q. Rewrite the following equation in standard form.

\newline

y = 10x + 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

.

Start with given equation: To rewrite the equation in standard form, we need to rearrange the terms so that the $x$ and $y$ terms are on the left side of the equation and the constant is on the right side. We start with the given equation: $\newline$ $y = 10x + 10$
Move $x$ term to other side: We want to move the term involving $x$ to the other side of the equation. To do this, we can subtract $10x$ from both sides of the equation: $\newline$ $y - 10x = 10x + 10 - 10x$
Simplify right side: Simplifying the right side of the equation, we get: $\newline$ $y - 10x = 10$ $\newline$ This is almost in standard form, but the terms on the left side are not in the conventional order.
Rearrange terms in standard form: The standard form of a linear equation is $Ax + By = C$ . We need to rearrange the terms on the left side to reflect this order: $\newline$ $-10x + y = 10$
Make coefficient A positive: However, the coefficient $A$ in standard form should be positive. To achieve this, we can multiply the entire equation by $-1$ : $\newline$ $-1(-10x + y) = -1(10)$
Make coefficient A positive: However, the coefficient $A$ in standard form should be positive. To achieve this, we can multiply the entire equation by $-1$ : $\newline$ $-1(-10x + y) = -1(10)$ Multiplying through, we get: $\newline$ $10x - y = -10$ $\newline$ Now the equation is in standard form with $A$ positive.

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