We start with the given equation:

$y - 3 = 4(x - 2)$

Step 1: Expand the equation

Expand the right-hand side:

$y - 3 = 4x - 8$

Step 2: Isolate the $y$-term

Add 3 to both sides to get $y$ by itself:

$y = 4x - 8 + 3$ $y = 4x - 5$

Step 3: Rearrange to standard form

To write the equation in standard form $Ax + By = C$, move the $4x$ to the left-hand side by subtracting $4x$ from both sides:

$-4x + y = -5$

Final Equation:

$-4x + y = -5$

The correct option is:

$\boxed{-4x + y = -5}$

Would you like further details or have any questions?

Here are 5 related questions to extend your understanding:

1. How would you convert an equation to slope-intercept form?
2. What does the slope represent in the equation $y = mx + b$?
3. How do you determine the x- and y-intercepts of a linear equation?
4. How can you solve systems of equations using substitution or elimination?
5. What is the geometric interpretation of a linear equation in two variables?

Tip: Standard form of a linear equation is typically written as $Ax + By = C$, where $A$, $B$, and $C$ are integers and $A$ should ideally be positive.