The pitch of the roof is the number of feet the roof rises for each 12 feet horizontally. if a roof has a pitch of 8. what is its slope expressed as a positive number? what does the slope mean in this story?

Refer to the diagram shown below.

The height is h ft
Half of the total horizontal base length is w ft.

Because the pitch is 8, therefore
When w = 12 ft, then h = 8 ft.
That is
w/h = 12/8
w = 1.5h

The slope is h/w = 8/12 = 2/3.
As an angle, 
θ = tan⁻¹ 2/3 = 33.7°

Slope = 2/3.
The slope represents an angle of elevation of 33.7°.