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Rewrite the following equation in standard form. $\newline$ $y = 7x + 8$ $\newline$ 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 = 7x + 8

\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

.

Move $x$ term to left: To rewrite the equation in standard form, we need to get the $x$ and $y$ terms on one side and the constant on the other side. We start with the given equation: $\newline$ $y = 7x - 8$ $\newline$ We want to move the $7x$ to the other side to isolate the $y$ term.
Subtract $7x$ : Subtract $7x$ from both sides of the equation to move the $x$ term to the left side: $\newline$ $y - 7x = -8$ $\newline$ This is not the standard form yet because the $x$ term should be before the $y$ term.
Rearrange terms: Rearrange the terms to put the $x$ term first: $\newline$ $-7x + y = -8$ $\newline$ Now, we have the $x$ term first, but the coefficient of $x$ is negative. In standard form, the coefficient of $x$ should be positive if possible.
Make $x$ coefficient positive: Multiply the entire equation by $-1$ to make the coefficient of $x$ positive: $\newline$ $-1(-7x + y) = -1(-8)$ $\newline$ $7x - y = 8$ $\newline$ Now the equation is in standard form, with $A = 7$ , $B = -1$ , and $C = 8$ .

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