Write an equation of a line in slope intercept form that is parallel to the line x + 4y = 6 and passes through (-8, 5)

If the line is parallel, then their slope would be equal.
4y = -x + 6
y = -1/4 x + 3/2

Compare it with, y = mx + b
m = -1/4 [ Slope ]

Now, y - y1 = m(x - x1)
y - 5 = -1/4 (x + 8)
y - 5 = -1/4x - 2
y = -1/4x + 3

In short, Your Answer would be: y = -1/4x + 3

Hope this helps!