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The given equation is:

\[
y - 4 = -6(x - 1)
\]

We are tasked with rewriting it in the standard form \( Ax + By = C \) where \( A, B, \) and \( C \) are integers.

### Step 1: Expand the equation
Expand the right-hand side of the equation:
\[
y - 4 = -6x + 6
\]

### Step 2: Rearrange terms to get \( Ax + By = C \)
Bring all terms to one side of the equation:
\[
6x + y = 10
\]

### Final Answer:
\[
6x + y = 10
\]

Here, \( A = 6 \), \( B = 1 \), and \( C = 10 \).

Would you like a detailed explanation of this process? Let me know if you have questions or need further clarification!

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### Related Questions:
1. What are the advantages of writing equations in \( Ax + By = C \) form?
2. How do you determine if an equation is already in standard form?
3. Can you convert \( Ax + By = C \) form to slope-intercept form (\( y = mx + b \))?
4. What are the properties of coefficients \( A, B, \) and \( C \) in a linear equation?
5. How would this process differ for fractional coefficients?

### Tip:
Always simplify equations so that \( A, B, \) and \( C \) are integers with \( A \) being positive, as this is the convention for standard form!

Rewrite the equation y - 4 = -6(x - 1) in Ax + By = C form. Use integers for A, B, and C.

Learn how to rewrite the linear equation y - 4 = -6(x - 1) into standard form Ax + By = C. Follow step-by-step guidance, applying the distributive property and rearranging terms to achieve the final equation 6x + y = 10. Ideal for students in Grades 8-10.

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