Question

the pitch of a roof is defined as $\frac{rise}{rafter}$.
(a) determine the pitch of the roof shown.
(b) determine the slope of the line - segment from point $d$ to point $e$
part 1 of 2
the pitch is $\frac{1}{8}$
part 2 of 2
the slope of the line segment from point $d$ to point $e$ is

Explanation:

Step1: Recall slope formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. In the context of the roof, if we consider point $D$ as the starting - point and $E$ as the ending - point, the rise is the vertical change and the run is the horizontal change. The rise from $D$ to $E$ is 3 ft and the run (half of the rafter length since we are going from the end - point of the rafter to the peak) is 12 ft (because the rafter length is 24 ft).

Step2: Calculate the slope

Using the slope formula $m=\frac{\text{rise}}{\text{run}}$, substituting the rise = 3 ft and run = 12 ft, we get $m=\frac{3}{12}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$