Take west to be the positive direction. The height of a sloped roof above the place where I stand is h = 18 feet (see the figure below). If I move x = 5 feet west, the height is 10 feet. What is the slope?
To find the slope, you need to use the formula:
Slope = (change in height) / (change in horizontal distance)
In this case, the change in height is given as the difference between the initial height (h = 18 feet) and the final height (h = 10 feet):
Change in height = 10 feet - 18 feet = -8 feet
The change in horizontal distance is given as moving 5 feet to the west:
Change in horizontal distance = -5 feet
Note that we use a negative sign for the change in horizontal distance because we are moving to the west, which is in the negative direction.
Now we can plug these values into the formula to calculate the slope:
Slope = (-8 feet) / (-5 feet)
Since the negative sign appears in both the numerator and the denominator, they cancel each other out, and the slope can be simplified to:
Slope = 8/5
So, the slope of the sloped roof is 8/5.