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To convert the given equation \[ y - 6 = -\frac{1}{2}(x - 4) \] to the general form, we'll follow these steps:

1. **Distribute** \(-\frac{1}{2}\) on the right side:
   \[
   y - 6 = -\frac{1}{2}x + 2
   \]

2. **Isolate** \( y \) by adding 6 to both sides:
   \[
   y = -\frac{1}{2}x + 2 + 6
   \]
   \[
   y = -\frac{1}{2}x + 8
   \]

3. **Multiply** the entire equation by 2 to eliminate the fraction:
   \[
   2y = -x + 16
   \]

4. **Rearrange** the equation into the general form \( Ax + By + C = 0 \):
   \[
   x + 2y - 16 = 0
   \]

The general form of the given equation is \[ x + 2y - 16 = 0 \].

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

Here are 5 related questions:
1. What is the significance of the general form of a linear equation?
2. How do you convert a linear equation from point-slope form to slope-intercept form?
3. Can you find the slope and y-intercept from the general form \(Ax + By + C = 0\)?
4. How can you determine the x- and y-intercepts from the general form equation?
5. What are the advantages of using the general form of a line equation in solving geometric problems?

**Tip:** Always simplify fractions before converting equations to general form to make the process easier.

Convert y - 6 = -1/2(x - 4) to general form.

Learn how to convert the linear equation y - 6 = -1/2(x - 4) from point-slope form to the general form. This step-by-step guide covers algebraic concepts like equation distribution, isolating variables, and converting to the general form, suitable for students in Grades 9-11.

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