We are given the equation:

\[
y - 6 = \frac{1}{4}(x + 8)
\]

Let's solve for \( y \) by following these steps:

1. **Distribute** \( \frac{1}{4} \) on the right-hand side:
   \[
   y - 6 = \frac{1}{4}x + \frac{1}{4} \times 8
   \]
   \[
   y - 6 = \frac{1}{4}x + 2
   \]

2. **Add 6** to both sides to isolate \( y \):
   \[
   y = \frac{1}{4}x + 2 + 6
   \]
   \[
   y = \frac{1}{4}x + 8
   \]

Thus, the solution is:

\[
y = \frac{1}{4}x + 8
\]

This is the equation of a line in slope-intercept form, where the slope is \( \frac{1}{4} \) and the y-intercept is 8.

Would you like more details or further explanation?

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Here are 5 related questions:

1. What is the slope and y-intercept of the equation \( y = \frac{1}{4}x + 8 \)?
2. How do you convert a point-slope equation into slope-intercept form?
3. What is the significance of the slope in linear equations?
4. How would you graph the equation \( y = \frac{1}{4}x + 8 \)?
5. How do parallel lines compare in terms of their slopes?

**Tip:** In any linear equation, the coefficient of \(x\) represents the slope, showing how steep the line is.

Learn how to solve the linear equation y = (1/4)x + 8 with a detailed step-by-step solution. This problem covers key algebraic concepts, including linear equations and the slope-intercept form. Suitable for students in Grades 7-9.

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