convert y-4 = -1/2(x-6) into general form

To convert the equation \( y - 4 = -\frac{1}{2}(x - 6) \) into general form, we need to rearrange it into the form \( Ax + By + C = 0 \).

Here's the step-by-step process:

1. Start with the given equation:
   \[
   y - 4 = -\frac{1}{2}(x - 6)
   \]

2. Distribute the \(-\frac{1}{2}\) on the right-hand side:
   \[
   y - 4 = -\frac{1}{2}x + 3
   \]

3. Add 4 to both sides to isolate \(y\):
   \[
   y = -\frac{1}{2}x + 3 + 4
   \]
   \[
   y = -\frac{1}{2}x + 7
   \]

4. Rearrange to move all terms to one side of the equation to get the general form:
   \[
   \frac{1}{2}x + y - 7 = 0
   \]

5. To eliminate the fraction, multiply every term by 2:
   \[
   x + 2y - 14 = 0
   \]

So, the equation \( y - 4 = -\frac{1}{2}(x - 6) \) in general form is:
\[
x + 2y - 14 = 0
\]

Would you like more details or have any questions?

Here are 8 relative questions expanding on this information:
1. How do you convert an equation from point-slope form to slope-intercept form?
2. What is the process for converting slope-intercept form to general form?
3. Can you explain the significance of the general form of a linear equation?
4. How do you find the x-intercept and y-intercept from the general form of a linear equation?
5. What are the steps to graph a linear equation given in general form?
6. How can you determine if two linear equations are parallel or perpendicular from their general forms?
7. What is the standard form of a linear equation and how does it differ from the general form?
8. How do you solve a system of linear equations when both equations are in general form?

**Tip:** Always check your final equation to ensure it doesn't contain any fractions or decimals, as the general form typically uses integers for simplicity.

Learn how to convert the equation y - 4 = -1/2(x - 6) into general form with a detailed step-by-step solution. This problem covers key concepts in linear equations and equation transformations. Suitable for students in Grades 7-9.

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