The given equation is:

$y = 10x - 2$

We are tasked with rewriting this equation in standard form, which is:

$Ax + By = C$

Step-by-Step Solution:

1. Start with the given equation: $y = 10x - 2$

2. Rearrange the equation so that both $x$ and $y$ terms are on the left side: $-10x + y = -2$

3. To ensure that the coefficient of $x$ is positive, multiply the entire equation by $-1$: $10x - y = 2$

Now, the equation is in standard form: $10x - y = 2$, where $A = 10$, $B = -1$, and $C = 2$. The greatest common factor (GCF) of these values is 1, satisfying the requirements.

Would you like any further details or have any questions about this solution?

Here are 5 related questions to expand your understanding:

1. How can you convert a slope-intercept form equation to standard form in general?
2. Why is it necessary to have integers for $A$, $B$, and $C$ in the standard form?
3. How does the sign of $A$ affect the standard form of a linear equation?
4. What is the difference between standard form and slope-intercept form?
5. Can a vertical line equation be written in standard form?

Tip: When converting to standard form, it's common practice to keep the coefficient of $x$ positive for clarity and consistency.