Take west to be the positive direction. The height of a sloped roof above the place where I stand is h = 12 feet (see the figure below).
If I move 3 feet west, the height is 10 feet. If I move 2 additional feet west, what is the height of the roof above the place where I stand?
No figure given. Cannot copy and paste here.
To find the height of the roof above the place where you stand after moving an additional 2 feet west, let's analyze the given information.
We know that when you move 3 feet west, the height of the roof is 10 feet. This means that there is a constant rate of change in the height of the roof as you move westward.
Using this information, we can determine the rate at which the height changes. The change in the height (Δh) divided by the change in distance (Δd) will give us the rate of change, which we can denote as "m".
Given:
Δh = -2 feet (decrease in height)
Δd = -2 feet (decrease in distance, since we are moving west)
Now, using the slope formula:
m = Δh / Δd
Substituting the given values, we have:
m = -2 feet / -2 feet
m = 1
The slope of the roof is 1, which means that for every 1 foot you move west, the height of the roof decreases by 1 foot.
Therefore, if you move an additional 2 feet west from the initial position (where the height is 10 feet), the height of the roof will be:
h = initial height - (m * distance)
h = 10 feet - (1 foot * 2 feet)
h = 10 feet - 2 feet
h = 8 feet
So, the height of the roof above the place where you stand, after moving an additional 2 feet west, is 8 feet.