Consider the line =+3x6y−8 . what is the slope of a line parallel to this line? what is the slope of a line perpendicular to this line?

Two lines are parallel if their slope is the same.
You want to write 8x + 4y = 5 in the form y = mx + b, where m represents the slope and b is the y-intercept.
We need to isolate y in the given equation. The number next to x is the slope.
8x + 4y = 5
4y = -8x + 5

y = (-8x +5)/4
y = -2x + 5/4
The slope of the line we want is -2.
Two lines are perpendicular if the slope of the first line times the slope of the second line produces a product of negative one.
Since our slope is -2, we know that -2 times 1/2 yields -1.
The slope of the line perpendicular is 1/2.