https://file.aiquickdraw.com/mathbot/file/17258905189252406uvai.jpg

The equation provided is:

\[
y = \frac{2}{3}x + \frac{1}{6}
\]

To transform this into the general form of a linear equation, \(Ax + By + C = 0\), we can follow these steps:

1. Start with the given equation:
   \[
   y = \frac{2}{3}x + \frac{1}{6}
   \]

2. Subtract \(\frac{2}{3}x\) from both sides to move the \(x\)-term to the left:
   \[
   y - \frac{2}{3}x = \frac{1}{6}
   \]

3. Multiply the entire equation by 6 to eliminate the fractions:
   \[
   6y - 4x = 1
   \]

4. Rearrange the equation to match the general form \(Ax + By + C = 0\):
   \[
   -4x + 6y - 1 = 0
   \]
   Or, multiplying through by -1 to simplify:
   \[
   4x - 6y + 1 = 0
   \]

Thus, the general form of the equation is:

\[
4x - 6y + 1 = 0
\]

Let me know if you would like further clarification!

Here are five related questions to explore:

1. How do we derive the slope from the general form of a linear equation?
2. What is the significance of the constant term in the general form?
3. Can you convert a general form equation back to slope-intercept form?
4. How would you graph the general form equation on a Cartesian plane?
5. What are the advantages of using different forms (slope-intercept vs. general form)?

**Tip**: Always check that your equation is simplified and in the correct format for the form you are working with, especially when working with fractions!

Transform this to general form: y = (2/3)x + 1/6

Learn how to transform the linear equation y = (2/3)x + 1/6 into its general form, Ax + By + C = 0. This step-by-step guide is ideal for students in Grades 8-10, covering key algebraic concepts.

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