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.