The problem asks us to rewrite the equation $y = x + 9$ in standard form, which is $Ax + By = C$, where $A$, $B$, and $C$ are integers and the greatest common factor (GCF) of $A$, $B$, and $C$ is 1.

1. Problem Description

The problem asks us to rewrite the equation $y = x + 9$ in standard form, which is $Ax + By = C$, where $A$, $B$, and $C$ are integers and the greatest common factor (GCF) of $A$, $B$, and $C$ is

1.

2. Solution Steps

We are given the equation $y = x + 9$. To rewrite this in the form $Ax + By = C$, we need to move the $x$ term to the left side of the equation. We can subtract $x$ from both sides of the equation:

$y - x = x + 9 - x$

$y - x = 9$

$-x + y = 9$

To follow convention, we usually write the $x$ term first, and we want $A$ to be positive if possible. We can multiply the whole equation by $-1$:

$-1(-x + y) = -1(9)$

$x - y = -9$

Now, $A = 1$, $B = -1$, and $C = -9$. The GCF of 1, -1, and -9 is

1. So the standard form is $x - y = -9$.

3. Final Answer

$x - y = -9$