Final answer:
Roofing gutters should slope at a vertical drop of 1/4-inch per 5 to 10 feet of gutter length. This translates to a slope of about 1/16-inch to 1/32-inch per foot. The ratio for scale to actual distance is 1/2 inch to 5 feet.
Step-by-step explanation:
The question is asking for the slope that roofing gutters should have to ensure proper drainage towards the downspout. A common guideline for gutter slope is a vertical drop of 1/4-inch for every 5 to 10 feet of horizontal gutter run. To express this as a rate per foot, one could say that for every foot of the gutter, there should be approximately 1/16-inch to 1/32-inch of slope, depending on whether one subscribes to the 5-foot or 10-foot guideline respectively. The equation to express this is inches/feet = 0.5/5 or 0.5/10 for the shorter or longer span, respectively.
To demonstrate this with ratios, one would write the scale distance to the actual distance as follows: 1/2 inch (scale distance) is to 5 feet (actual distance) as X inches (unknown scale distance) is to Y feet (actual known distance of gutter length).