Write $y-2=\frac{1}{3}\left(x+6\right)$
 in standard form.
An equation is 
.

To convert the equation $ y - 2 = \frac{1}{3}(x + 6) $ into standard form, we follow these steps:

1. Distribute $\frac{1}{3}$:
   \[
   y - 2 = \frac{1}{3}x + 2
   \]

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

3. To convert to standard form $Ax + By = C$, we eliminate the fraction by multiplying the entire equation by 3:
   \[
   3y = x + 12
   \]

4. Rearranging gives:
   \[
   -x + 3y = 12
   \]

5. Finally, we can write this as:
   \[
   x - 3y = -12
   \]

Thus, the equation in standard form is:
\[
x - 3y = -12
\]

Would you like more details or have any questions about the steps? Here are some related questions you might consider:

1. What is the significance of standard form in linear equations?
2. How can you determine the slope and y-intercept from standard form?
3. Can you explain how to convert from standard form back to slope-intercept form?
4. What are the characteristics of lines represented by equations in standard form?
5. How does changing the coefficients in the standard form affect the graph of the equation?

**Tip:** Always check your work by substituting a point back into the original equation to see if it holds true.

Write $y-2=\frac{1}{3}\left(x+6\right)$ in standard form.

Learn how to convert the equation y - 2 = (1/3)(x + 6) into standard form with a detailed step-by-step solution. This problem involves key algebraic concepts and is suitable for students in Grades 8-10.

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